Trees of semi-simple algebras

Details Trees of semi-simple algebras Trees of semi-simple algebras

2005-07-25

arxiv.org/abs/math/0507503v1

Mathematics

Rings and Algebras

Scientific paper

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.

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