Trees of semi-simple algebrasTrees of semi-simple algebras
Faculty of Sciences. Mathematics and Computer Science

Fundamental Mathematics

Department of Mathematics - Computer Sciences

article

2005 2005

Mathematics

eprint-archive math.RA

(2005), p. 0507503,1-0507503,26

1

E

English (eng)

University of Antwerp

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.

http://arxiv.org/abs/math.RA/0507503