Title
Trees of semi-simple algebras Trees of semi-simple algebras
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Source (journal)
eprint-archive math.RA
Volume/pages
(2005) , p. 0507503,1-0507503,26
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
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.
E-info
http://arxiv.org/abs/math.RA/0507503
Handle