Lieven Le Bruyn's Publications

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• 2020 • 2019 • 2018 • 2017 • 2016 • 2015 • 2014 • 2013 • 2012 • 2011 • 2010 • 2009 • 2008 • 2007 • 2006 • 2005 • 2004 • 2003 • 2002 • 2001 • 2000 • 1999 • 1998 • 1997 • 1996 • 1995 • 1994 • 1993 • 1992 • 1991 • 1990 • 1989 • 1988 • 1987 • 1986 • 1985 • 1984 • 1983 • 1982 • 1981 • 1980 •

2020

• Lieven LeBruyn. Three arithmetic sites. arXiv/math.AG, 2003.01387:, 2020.
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• Lieven LeBruyn. Counting in times of fake fields. arXiv/math.AG, 2004.05907:, 2020.
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2019

• Karin Cvetko-Vah, Jens Hemelaer, and Lieven LeBruyn. Duality for noncommutative frames. arXiv/math.RA, 1901.10243:, 2019.
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• Jens Hemelaer and Lieven LeBruyn. Azumaya geometry and representation stacks. arXiv/math.RT, 1606.07885v3:, 2019.
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• Lieven LeBruyn. Motivic measures and F1-geometry. arXiv/math.AG, 1901.10243:, 2019.
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• Lieven LeBruyn. Virtual representation motives. arXiv/math.RT, 1904.12536:, 2019.
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2018

• Karin Cvetko-Vah, Jens Hemelaer, and Lieven LeBruyn. What is a noncommutative topos?. Journal of Algebra & Its Applications, ISSN 0219-4988 :1–18, 2018.
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• Lieven LeBruyn. Brauer-Severi motives and Donaldson-Thomas invariants of quantized threefolds . Journal of noncommutative geometry, 12:2 :671–692, 2018.
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• Lieven LeBruyn. The monstrous moonshine picture. arXiv/math.GR, 1804.04127:, 2018.
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2017

• Karin Cvetko-Vah, Jens Hemelaer, and Lieven LeBruyn. What is a noncommutative topos?. arXiv/math.RA, 1705.02831:, 2017.
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• Lieven LeBruyn. The superpotential XYZ+XZY+c(X^3+Y^3+Z^3). arXiv/math.RA, 1705.03243:, 2017.
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• Lieven LeBruyn. Linear recursive sequences and Spec(?) over F1. Communications in algebra, 45:3150–3158, 2017.
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2016

• Pieter Belmans, Kevin DeLaet, and Lieven LeBruyn. The point variety of quantum polynomial rings. Journal of Algebra, 463:10–22, 2016.
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• Jens Hemelaer and Lieven LeBruyn. Azumaya representation schemes. arXiv/math.RA, 1606.07885:, 2016.
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• Lieven LeBruyn. The sieve topology on the arithmetic site. Journal of Algebra and Its Applications, 15:, 2016.
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• Lieven LeBruyn. Bulk irreducibles of the modular group. Journal of Algebra and Its Applications, 15:, 2016.
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• Lieven LeBruyn. Extending irreducible braid representations to the 3-component loopbraid group. International Journal of Mathematics and Computer Science, 11:81–87, 2016.
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• Lieven LeBruyn. Absolute geometry and the Habiro topology. In Absolute arithmetic and F1-geometry, pp. 220–271, EMS Publishing House ISBN print 978-3-03719-157-6, DOI 10.4171/157 , 2016.
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• Lieven LeBruyn. Covers of the arithmetic site. arXiv/math.RA, 1602.01627:, 2016.
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• Lieven LeBruyn. Brauer Severi motives and Donaldson Thomas invariants of quantized 3-folds. arXiv/math.RT, 1604.08556:, 2016.
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2015

• Pieter Belmans, Kevin DeLaet, and Lieven LeBruyn. The point variety of quantum polynomial rings. arXiv/math.RA, 1509.07312:, 2015.
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• Kevin DeLaet and Lieven LeBruyn. Point modules of quantum projective spaces. arXiv/math.RT, 1506.0651:, 2015.
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• Kevin DeLaet and Lieven LeBruyn. The geometry of representations of the 3-dimensional Sklyanin algebras. Algebras and Representation Theory, 18:761–776, 2015.
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• Lieven LeBruyn. High dimensional representations of the 3-component loop braid group. arXiv/math.RA, 1508.00871:, 2015.
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• Lieven LeBruyn. The coordinate biring of Spec(Z)/F_1. arXiv/math.RA, 1509.00749:, 2015.
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2014

• Lieven LeBruyn and Kevin DeLaet. The geometry of representations of 3-dimensional Sklyanin algebras. arXiv/math.RA, 1405.1158:, 2014.
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• Lieven LeBruyn. Supernatural numbers and a new topology on the arithmetic site. arXiv/math.RA, 1407.5538:, 2014.
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• Lieven LeBruyn. The singularities of noncommutative manifolds. arXiv/math.RA, 1409.5867:, 2014.
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2013

• Lieven LeBruyn. Matrix transposition and braid reversion. Journal of Pure and Applied Algebra, 217:75–81, 2013. published version of LeBruyn2011a
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• Lieven LeBruyn. Absolute geometry and the Habiro topology. arXiv/math.RA, 1304.6532:, 2013. 50 pages
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• Lieven LeBruyn. Most irreducible representations of the 3-string braid group. arXiv/math.RA, 1303.4907:, 2013.
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2012

• Lieven LeBruyn. Monsters and Moonshine, 2012. 114 pages
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• Lieven LeBruyn. Algebraic D-branes. Unpublished 2012. Talk Lorentz-Institute, March 2012
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• Lieven LeBruyn. Noncommutative F_1-geometry. Unpublished 2012. Talk European Congress of Mathematics, Krakow, July 2012
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2011

• Lieven LeBruyn. Matrix transposition and braid reversion. arXiv/math.RA, 1102.4188, 2011.
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• Lieven LeBruyn. The Bourbaki Code, 2011. 38 pages
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• Lieven LeBruyn. Absolute Geometry, 2011. 69 pages
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• Lieven LeBruyn. Dense families of B3-representations and braid reversion. Journal of Pure and Applied Algebra, 215:1003–1014, 2011. published version of LeBruyn2010a
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2010

• Lieven LeBruyn. Rationality and dense families of B(3) representations. arXiv/math.RA, 1003.1610, 2010.
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• Lieven LeBruyn. Representation stacks, D-branes and noncommutative geometry. arXiv/math.RA, 1009.5203, 2010.
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• Lieven LeBruyn. Algebraic D-branes. Unpublished 2010. Talk ART-seminar may 2009, Antwerp
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• Lieven LeBruyn. Hoe ziet een priemgetal eruit?. Unpublished 2010. Talk alumni-day, april 1st 2010, Antwerp
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2009

• Lieven LeBruyn. (non)commutative f-un geometry. arXiv/math.RA, 0909.2522, 2009.
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• Lieven LeBruyn. Noncommutative geometry over the field with one element. Unpublished 2009. Talk ART-seminar march 2009, Antwerp
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• Lieven LeBruyn. From zeroes to stacks in 2 hours. Unpublished 2009. Talk summer-school july 2009, Antwerp
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2008

• Lieven LeBruyn. Braid group B(3) irreducibles - a DIY guide. arXiv/math.QA, 0803.3601, 2008.
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• Lieven LeBruyn. Noncommutative geometry and dual coalgebras. arXiv/math.QA, 0805.2377, 2008.
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• Lieven LeBruyn. Halloween talk : the fields with one element and other ghost stories. Unpublished 2008. Talk ART-seminar on halloween 2008, Antwerp
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• Lieven LeBruyn. Affine geometry over the field with one element. Unpublished 2008. Talk ART-seminar on 21 november 2008, Antwerp
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2007

• Lieven LeBruyn. Noncommutative Geometry and Cayley-smooth Orders, Pure and Applied Mathematics 290, Chapman and Hall / CRC, 2007. 592 pages
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• Lieven LeBruyn. Inleiding Groepentheorie, 2007.
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• Lieven LeBruyn. Representaties van Eindige Groepen, 2007.
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2006

• Cristof Geiss, Lieven LeBruyn, and Markus Reineke. Introduction to moduli spaces associated to quivers (with an appendix by Lieven Le Bruyn and Markus Reineke. Contemporary Mathematics, 406:31–50, 2006.
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• Lieven LeBruyn. Non-commutative algebraic geometry and commutative desingularizations. Lecture Notes in Pure and Applied Mathematics, 243:203–252, 2006. also available as 'Three talks on noncommutative geometry@n' math.RA/0312221
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• Lieven LeBruyn. Elementaire Algebraische Meetkunde, 2006.
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2005

• Jan Adriaenssens and Lieven LeBruyn. Trees of semi-simple algebras. arXiv/math.RA, 0507503:, 2005. math.RA/0507503
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• Lieven LeBruyn. Qurves and Quivers. Journal of Algebra, 290:447–472, 2005. math.RA/0406618
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• Lieven LeBruyn and Stijn Symens. Partial desingularizations arising from non-commutative algebras. arXiv/math.RA, 0507494:, 2005. math.RA/0507494
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• Lieven LeBruyn. noncommutative geometry@n, volume 2 : the trade, neverendingbooks, 2005.
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• Lieven LeBruyn. noncommutative geometry@n, volume 1 : the tools, neverendingbooks, 2005.
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• Lieven LeBruyn. COLgo en SNORTgo : inleiding tot combinatorische speltheorie. Unpublished 2005. Talk to undergraduates on combinatorial game theory
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• Lieven LeBruyn. Noncommutative geometry and topological D-branes. Unpublished 2005. Talks on Lazaroiu's paper for IP september 2005, Antwerp
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• Lieven LeBruyn. Granada NAG : Examples in Noncommutative Geometry, 2005. Talks given in Granada, April 2005
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2004

• Lieven LeBruyn. Representations of virtually free groups. Unpublished 2004.
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• Lieven LeBruyn. Cursus Meetkunde 1, 2004. Course notes of a Geometry 101 course
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• Lieven LeBruyn. Brauer-Severi schemes of smooth orders. Unpublished 2004. Notes of talk given in Warwick
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• Lieven LeBruyn. Quotient singularities and the conifold algebra, 2004. Talks NOG-masterclass 2004
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• Lieven LeBruyn. NOG-masterclass 2004, 2004. Notes for masterclass 2004
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2003

• Jan Adriaenssens and Lieven LeBruyn. Local quivers and stable representations. Communications in Algebra, 31:1777–1797, 2003. math.RT/0010251
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• Jan Adriaenssens and Lieven LeBruyn. Non-commutative covers and the modular group. arXiv/math.RA, 0307139:, 2003. math.RA/0307139
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• Raf Bocklandt, Lieven LeBruyn, and Geert VandeWeyer. Smooth order singularities. Journal of Algebra and its Applications, 2:365–395, 2003. small version at math.RA/0207250
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• Raf Bocklandt, Lieven LeBruyn, and Stijn Symens. Isolated singularities, smooth orders and Auslander regularity. Communications in Algebra, 31:6019–6036, 2003. math.RA/0207251
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• Lieven LeBruyn and Markus Reineke. Canonical systems and non-commutative geometry. arXiv/math.AG, 0303304:, 2003. math.AG/0303304
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• Lieven LeBruyn. One quiver to rule them all. arXiv/math.RA, 0304196:, 2003. math.RA/0304196
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• Lieven LeBruyn. A non-commutative topology on rep(A). arXiv/math.RA, 0307138:, 2003. math.RA/0307138
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• Lieven LeBruyn. Noncommutative etale and Zariski topologies. Unpublished 2003. Notes of talk given for Algebra Seminar in Antwerp
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2002

• Raf Bocklandt and Lieven LeBruyn. Necklace Lie algebras and noncommutative symplectic geometry. Mathematische Zeitschrift, 240:141–167, 2002. math.AG/0010030
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• Lieven LeBruyn and Geert VandeWeyer. Formal structures and representation spaces. Journal of Algebra, 247:616–635, 2002. math.RA/0101231
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• Lieven LeBruyn. Noncommutative smoothness and coadjoint orbits. Journal of Algebra, 258:60–70, 2002. math.AG/0107028
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• Lieven LeBruyn. Noncommutative smooth models. arXiv/math.RA, 0209067:, 2002. math.RA/0209067
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• Lieven LeBruyn. noncommutative geometry@n (version3), neverendingbooks, forgotten books department, 2002.
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• Lieven LeBruyn. The essential GIT & PI, 2002. NOG masterclass course 2002
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2001

• Lieven LeBruyn. Optimal filtrations on representations of finite dimensional algebras. Transactions of the American Mathematical Society, 353:411–426, 2001. UIA report 98-08
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• Lieven LeBruyn. Simple roots of deformed preprojective algebras. arXiv/math.RA, 0107027:, 2001. math.RA/0107027
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• Lieven LeBruyn. Cursus Logica, 2001. Course notes of a Logic course
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• Lieven LeBruyn. Quivervarieties are diffeomorphic to coadjoint orbits. Unpublished 2001. Notes of talks for Summerschool NOG, 2001 in Antwerp
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2000

• Lieven LeBruyn. Local structure of Schelter-Procesi smooth orders. Transactions of the American Mathematical Society, 352:4815–4841, 2000. UIA report 97-05
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• Lieven LeBruyn. The singularities of quantum groups. Proceedings of the London Mathematical Society, 80:304–336, 2000. UIA report 98-07
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• Lieven LeBruyn. noncommutative geometry@n (version 2), neverendingbooks, forgotten books department, 2000.
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• Lieven LeBruyn. Noncommutative Geometry and Operads. Unpublished 2000. Slides of talks at Isle of Thorns, UK 2000
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1999

• Stefaan Caenepeel, Sorin Dacalescu, and Lieven LeBruyn. Forms of pointed Hopf algebras. Manuscripta Mathematica, 100:35–53, 1999. UIA report 98-15
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• Lieven LeBruyn and George Seelinger. Fibers of generic Brauer-Severi schemes. Journal of Algebra, 214:222–234, 1999. UIA report 97-01
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• Lieven LeBruyn and Zinovy Reichstein. Smoothness in algebraic geography. Proceedings of the London Mathematical Society, 79:158–190, 1999. UIA report 97-11
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• Lieven LeBruyn. Noncommutative geometry at n. arXiv/math.AG, 9904171:, 1999. math.AG/9904171
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• Lieven LeBruyn. noncommutative geometry@n (version 1), neverendingbooks, forgotten books department, 1999.
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• Lieven LeBruyn. Noncommutative compact manifolds constructed from quivers. AMA Algebra Montpellier Announcements, 1:1–5, 1999. math.AG/9907136
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• Lieven LeBruyn. Bonn Talk. Unpublished 1999. Talk given at MPI 1999
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• Lieven LeBruyn. Course notes Computational Geometry, 1999.
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• Lieven LeBruyn. Life after Kaplansky 10?. Unpublished 1999. Notes of a talk given in Brussels
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• Lieven LeBruyn. Course Geometric Invariant Theory, 1999. Undergraduate introduction to GIT
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1998

• Lieven LeBruyn. Generating graded central simple algebras. Linear Algebra and its Applications, 268:323–344, 1998. UIA report 96-19
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1997

• Lieven LeBruyn. Nilpotent representations. Journal of Algebra, 197:153–177, 1997. UIA report 95-16
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• Lieven LeBruyn. Orbits of matrix tuples. Seminaires Congres, Societe Mathematique de France, 2:245–261, 1997. UIA report 95-20
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• Lieven LeBruyn. Lie stacks and their enveloping algebras. Advances in Mathematics, 130:103–135, 1997. UIA report 96-02
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• Lieven LeBruyn. Lie stack deformations. Journal of Algebra, 196:552–577, 1997. UIA report 96-12
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• Lieven LeBruyn. Automorphisms and Lie stacks. Communications in Algebra, 25:2211–2226, 1997. UIA report 96-13
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• Lieven LeBruyn. Etale cohomology in noncommutative geometry, 1997. UIA report 97-04
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• Lieven LeBruyn. Degenerations of matrices and rationality. Unpublished 1997. UIA report 97-06
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1996

• Lieven LeBruyn, S. Paul Smith, and Michel VandenBergh. Central extensions of three-dimensional Artin-Schelter regular algebras. Mathematische Zeitschrift, 222:171–212, 1996. september 1994
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• Lieven LeBruyn. Counterexamples to the Gelfand-Kirillov conjecture (d'apres Alev-Ooms-VandenBergh). Unpublished 1996. Talk at UIA seminar
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1995

• Kristien Bauwens and Lieven LeBruyn. Some remarks on solvable Lie superalgebras. Journal of Pure and Applied Algebra, 99:113–134, 1995. UIA report 92-45
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• Lieven LeBruyn. Moduli spaces for right ideals of the Weyl algebra. Journal of Algebra, 172:32–48, 1995. UIA report 92-49
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• Lieven LeBruyn. Conformal sl(2)-algebras. Communications in Algebra, 23:1325–1362, 1995. UIA report 94-12
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• Lieven LeBruyn. Generic norm one tori. Nieuw Archief voor Wiskunde, 13:401–407, 1995. UIA report 94-22
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• Lieven LeBruyn. Central singularities of quantum spaces. Journal of Algebra, 177:142–153, 1995. UIA report 94-06
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• Lieven LeBruyn. The nullcone of quiver representations. Unpublished 1995. UIA report 95-14
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1994

• Lieven LeBruyn. The arithmetic of Sklyanin algebras 1 : the defining equations. Communications in Algebra, 22:51–81, 1994. UIA report 92-25
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• Lieven LeBruyn. Sklyanin algebras and their symbols. K-theory, 8:3–17, 1994. UIA report 92-56
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• Lieven LeBruyn. Two remarks on Witten's quantum enveloping algebra. Communications in Algebra, 22:865–876, 1994. UIA report 93-01
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• Lieven LeBruyn. Homological properties of braided matrices. Journal of Algebra, 170:596–607, 1994. UIA report 93-11
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• Lieven LeBruyn. Lie groepen en representatie tehorie, 1994. Course notes of a Lie group and representation theory course
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1993

• Lieven LeBruyn. Rational identities of matrices and a theorem of G. M. Bergman. Communications in Algebra, 21:2577–2581, 1993. UIA report 91-26
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• Lieven LeBruyn and S. Paul Smith. Homogenized sl(2). Proceedings of the American Mathematical Society, 118:725–730, 1993. UIA report 91-37
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• Lieven LeBruyn and Michel VandenBergh. On quantum spaces of Lie algebras. Proceedings American Mathematical Society, 119:407–414, 1993. UIA report 91-45
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• Lieven LeBruyn. Central singularities of certain quantum spaces. Unpublished 1993. UIA report 93-12
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1992

• Lieven LeBruyn and Fred VanOystaeyen. Quantum sections and gauge algebras. Publicacions Mathematiques, 36:693–714, 1992.
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• Lieven LeBruyn, Fred VanOystaeyen, and Luc Willaert. Quantum sections of schematic algebras. Unpublished 1992. UIA report 92-50
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1991

• Christine Bessenrodt and Lieven LeBruyn. Stable rationality of certain PGL(n) quotients. Inventiones Mathematicae, 104:179–199, 1991. UIA report 89-29
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• Lieven LeBruyn and Michel VandenBergh. Algebraic properties of linear cellular automata. Linear Algebra and its Applications, 157:217–234, 1991. UIA report 90-15
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• Lieven LeBruyn. Centers of generic division algebras, the rationality problem 1965-1990. Israel Journal of Mathematics, 76:97–111, 1991. UIA report 90-17
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• Lieven LeBruyn and Geert Molenberghs. Generic relative crossed products and universal division algebras. Unpublished 1991. UIA report 91-01
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• Lieven LeBruyn. Rational identities of matrices revisited. Unpublished 1991. UIA report 91-03
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1990

• Lieven LeBruyn and Claudio Procesi. Semi-simple representations of quivers. Transactions American Mathematical Society, 317:585–598, 1990. UIA report 88-02
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• Lieven LeBruyn and Yasuo Teranishi. Matrixinvariants and complete intersections. Glasgow Mathematical Journal, 32:227–229, 1990. UIA report 88-07
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• Lieven LeBruyn. Generic norm one tori. Unpublished 1990. UIA report 90-04
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1989

• Christine Bessenrodt and Lieven LeBruyn. Stable rationality of certain moduli spaces. Unpublished 1989. UIA report 89-21
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• Lieven LeBruyn. Simultaneous equivalence classes of square matrices. In Seminaire Malliavin, pp. 127–136, Lecture Notes in Mathematics 1404, 1989. UIA report 87-01
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• Lieven LeBruyn. Quiver concomitants are often reflexive Azumaya. Proceedings American Mathematical Society, 105:10–16, 1989. UIA report 87-23
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• Lieven LeBruyn and Geert Molenberghs. Centers of generic division algebras. Israel Mathematical Conference Proceedings, 1:310–319, 1989. UIA report 88-37
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• Lieven LeBruyn and Geert Molenberghs. Generic Brauer Algebras 1. Unpublished 1989. UIA report 89-40
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1988

• Lieven LeBruyn and Michel VandenBergh. Regularity of trace rings of generic matrices. Journal of Algebra, 117:19–29, 1988. UIA report 85-24
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• Lieven LeBruyn. Centers of generic division algebras and zeta-functions. In , pp. , Lecture Notes in Mathematics 1328, 1988. UIA report 86-24
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• Lieven LeBruyn and Aidan Schofield. Rational invariants of quivers and the ring of matrix invariants. In Perspectives in Ring Theory, pp. 21–29, NATO Advanced Science Institute 233, 1988. UIA report 87-07
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• Lieven LeBruyn. Some results on rational matrix invariants. Journal of Algebra, 118:487–493, 1988. UIA report 87-08
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• Lieven LeBruyn and Jacques Alev. Automorphisms of generic 2x2 matrices. In Perspectives in Ring Theory, pp. 69–83, NATO Advanced Science Institute 233, 1988. UIA report 87-18
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• Lieven LeBruyn and Fred VanOystaeyen. Brauer groups of fields, Lecture Notes in Mathematics 17, University of Essen, January 1988. UIA report 88-01
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• Lieven LeBruyn. Permutation modules and rationality problems 1, October 1988. UIA report 88-30
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• Lieven LeBruyn. On a conjecture of D. Luminet. Unpublished 1988. UIA report 88-08
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• Lieven LeBruyn, Michel VandenBergh, and Fred VanOystaeyen. Graded Orders, Birkhauser, June 1988.
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1987

• Lieven LeBruyn and Michel VandenBergh. The ramification divisor of regular tame orders 1. Communications in Algebra, 15:1815–1840, 1987. UIA report 84-08
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• Lieven LeBruyn. Trace rings of generic 2x2 matrices, Memoirs of the AMS 363, American Mathematical Society, 1987. UIA reports 84-27,84-28,84-30 and 84-31
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• Lieven LeBruyn. A cohomological interpretation of the reflexive Brauer group. Journal of Algebra, 105:250–254, 1987. UIA report 85-18
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• Lieven LeBruyn and Fred VanOystaeyen. A note on Clifford representations. Bulletin Belgisch Wiskundig Genootschap, 39:195–202, 1987. UIA report 85-21
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• Lieven LeBruyn and Claudio Procesi. Etale local structure of matrix invariants and concomitants. In , pp. , Lecture Notes in Mathematics 1271, 1987. UIA report 86-02
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• Lieven LeBruyn. The regularity problem for trace rings of generic matrices. Mededelingen Koninklijke Academie der Wetenschappen van Belgie, 49:1–23, 1987. UIA report 86-23
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• Lieven LeBruyn and Aidan Schofield. Rational invariants of quivers and the ring of matrix invariants. Unpublished 1987. UIA report 87-07
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• Lieven LeBruyn. Periodicity in additive linear cellular automata. Unpublished 1987. UIA report 87-25
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1986

• Lieven LeBruyn and Fred VanOystaeyen. A note on noncommutative Krull domains. Communications in Algebra, 14:1457–1472, 1986. UIA report 81-19 (May 1981)
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• Lieven LeBruyn. Quillen pathching for maximal orders. Communications in Algebra, 14:1679–1685, 1986. UIA report 83-13 (February 1983)
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• Lieven LeBruyn. Trace rings of generic matrices are unique factorization domains. Glasgow Mathematical Journal, 28:11–13, 1986. UIA report 84-10
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• Lieven ans Alain Verschoren LeBruyn. Maximal orders having a discrete normalizing class group. Journal of Algebra, 100:430–435, 1986. UIA report 84-15
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• Lieven LeBruyn. The Artin-Schofield theorem and some applications. Communications in Algebra, 14:1439–1455, 1986. UIA report 84-19
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• Lieven LeBruyn, Michel VandenBergh, and Fred VanOystaeyen. Proj of generic matrices and trace rings. Communications in Algebra, 14:1687–1706, 1986. UIA report 84-24
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• Lieven LeBruyn and Michel VandenBergh. An explicit description of T(3,2). In Ring Theory, Proceedings Antwerp 1985, pp. 109–113, Lecture Notes in Mathematics 1197, 1986. UIA report 84-26
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• Lieven LeBruyn. The Poincare series of T(m,2). In Ring Theory, Proceedings Antwerp 1985, pp. 90–108, Lecture Notes in Mathematics 1197, 1986.
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• Lieven LeBruyn. Cohomology of P(m,2). In Seminaire Malliavin, pp. 130–156, Lecture Notes in Mathematics 1220, 1986. UIA report 85-07
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• Lieven LeBruyn. Counterexamples to the Kac conjecture on Schur roots. Bulletin Sciences Mathematiques, 110:437–448, 1986. UIA report 86-13
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• Lieven LeBruyn. Some remarks on rational matrix invariants. Unpublished 1986. UIA report 86-30
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• Lieven LeBruyn. Global study of semi-simple representations of quivers. Unpublished 1986. UIA report 86-31
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1985

• Lieven LeBruyn. The Bass-Quillen conjecture and maximal orders. Bulletin Belgisch Wiskundig Genootschap, 37:37–45, 1985. UIA report 83-22 (May 1983)
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• Lieven LeBruyn and Alfons I. Ooms. The semi-center of an enveloping algebra is factorial. Proceedings American Mathematical Society, 93:397–400, 1985. UIA report 84-03
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• Lieven LeBruyn. The functional equation for Poincare series of trace rings of generic 2x2 matrices. Israel Journal of Mathematics, 52:355–360, 1985. UIA report 84-18
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• Lieven LeBruyn. Bijdrage tot het onderzoek naar de regulariteit van spoorringen van generieke matrixen, June 1985. UIA report 85-17
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1984

• Lieven LeBruyn. Class groups of maximal orders over Krull domains. Journal of Pure and Applied Algebra, 31:91–107, 1984.
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• Lieven LeBruyn. On the Jespers-VanOystaeyen conjecture. Journal of Algebra, 88:38–51, 1984. UIA report 82-32 (September 1982)
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• Lieven LeBruyn. Splitting by Galois objects. Bulletin Belgisch Wiskundig Genootschap, 36:155–170, 1984. UIA report 82-34 (September 1982)
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• Lieven LeBruyn. Smooth maximal orders in quaternion algebras 1. In Methods in Ring Theory, pp. 231–264, NATO Advanced Science Institute 129, 1984. UIA report 83-30 (September 1983)
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• Lieven LeBruyn. Homological properties of trace rings of generic matrices. Unpublished 1984. UIA report 84-02
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• Lieven LeBruyn. The trace ring of 2 generic 3x3 matrices is (not) regular. Unpublished 1984. UIA report 84-21, the result is wrong : this trace ring IS regular...
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1983

• Eric Jespers, Lieven LeBruyn, and Paul Wauters. A characterization of central Omega-Krull rings. Journal of Algebra, 81:165–179, 1983. UIA report 81-27 (July 1981)
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• Lieven LeBruyn. Towards a noncommutative version of the Bass-Tate sequence. Bulletin Belgisch Wiskundig Genootschap, 35:47–67, 1983. UIA report 82-04 (January 1982)
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• Lieven LeBruyn and Fred VanOystaeyen. Generalized Rees rings and relative maximal orders satisfying polynomial identities. Journal of Algebra, 83:409–436, 1983.
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• Lieven LeBruyn. A note on maximal orders over Krull domains. Journal of Pure and Applied Algebra, 28:241–248, 1983.
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• Lieven LeBruyn. Maximal orders having a discrete normalizing classgroup. Unpublished 1983. UIA report 83-32 (September 1983)
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• Lieven LeBruyn. On a problem of R.A. Hirschfeld. Unpublished 1983. UIA report 83-33 (September 1983)
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• Lieven LeBruyn. Class groups of maximal orders over Krull domains. Ph.D. Thesis, Universiteit Antwerpen, 1983.
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1982

• Eric Jespers, Lieven LeBruyn, and Paul Wauters. Omega-Krull rings 1. Communications in Algebra, 10:1801–1818, 1982. UIA report 81-26 (June 1981)
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• Lieven LeBruyn. Universal bialgebras associated with orders. Communications in Algebra, 10:457–478, 1982. UIA report 81-03 (February 1981), my first paper...
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• Lieven LeBruyn. Homogenization of sheaves and kernel functors. Bulletin Belgisch Wiskundig Genootschap, 34:241–265, 1982. UIA report 81-15 (May 1981)
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• Lieven LeBruyn. Arithmetical rings 2 : Relative normalizing classgroups. Unpublished 1982. UIA report 82-05 (January 1982)
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• Lieven LeBruyn. Faithfully flat descent and the Bass-Quillen conjecture. Unpublished 1982. UIA report 82-42, this paper contains errors, see the also items
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1981

• Lieven LeBruyn. A local-global approach to localization in Grothendieck categories. Unpublished 1981. UIA report 81-08 (February 1981)
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• Lieven LeBruyn. Arithmetical rings 1 : a unified approach to arithmetical theories. Unpublished 1981. UIA report 81-41 (November 1981)
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1980

• Lieven LeBruyn. Some ideas in noncommutative geometry. Master's Thesis, University of Antwerp,1980. My undergraduate thesis...
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