14/09/2017, 14.30 hs, aula 27 FaMAF

Poisson geometry of 3 dimensional PI Sklyanin algebras

Speaker: Milen Yakimov

Abstract: Many representation theoretic questions concern the structure of the representations of algebras which are module finite over their centers (universal enveloping algebras in prime characteristic, quantum groups at roots of unity, PI Sklyanin algebras). If such algebras can be equipped with the structure of Poisson orders in the sense of Brown and Gordon, then one can use Poisson geometry to get substantial information about their representations. We will describe a method of higher specializations and apply it to obtain structures of Poisson orders on the 3d PI Sklyanin algebras. This will be used to describe the irreducible representations of these algebras. This is a joint work with Chelsea Walton and Xingting Wang (UIUC).