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Jan Adriaenssens and Lieven LeBruyn. Trees of semi-simple algebras. arXiv/math.RA, 0507503:, 2005. math.RA/0507503
To a tree of semi-simple algebras we associate a qurve (or formally smooth algebra) S. We introduce a Zariski- and etale quiver describing the finite dimensional representations of S. In particular, we show that all quotient varieties of the etale quiver have a natural Poisson structure induced by a double Poisson algebra structure on a certain universal localization of its path algebra. Explicit calculations are included for the group algebras of the arithmetic groups (P)SL2(Z) and GL2(Z) but the methods apply as well to congruence subgroups.
@article{LeBruyn2005b,
author={Jan Adriaenssens and LeBruyn, Lieven},
title={Trees of semi-simple algebras},
abstract={To a tree of semi-simple algebras we associate a qurve
(or formally smooth algebra) S. We introduce a Zariski- and etale quiver
describing the finite dimensional representations of S. In particular,
we show that all quotient varieties of the etale quiver have a natural
Poisson structure induced by a double Poisson algebra structure on a certain
universal localization of its path algebra. Explicit calculations are included
for the group algebras of the arithmetic groups (P)SL2(Z) and GL2(Z) but
the methods apply as well to congruence subgroups.},
journal={arXiv/math.RA},
volume={0507503},
year={2005},
bib2html_pubtype ={Papers},
bib2html_rescat ={Noncommutative Geometry},
bib2html_dl_html={http://arxiv.org/abs/math.RA/0507503},
pages={},
language={English},
note={math.RA/0507503}
}
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