Xiao-Wu Chen (USTC, Hefei), Skew group categories, algebras associated to Cartan matrices and folding of root lattices.

Abstract:

It is well known that a symmetrizable Cartan matrix is related to a graph with automorphism, which gives rise to the folding between the root lattices. We construct an additive functor between certain module categories, viewed as some kind of categorification of the folding, which compares Gabriel's realization of the root system of a symmetric Cartan matrix of finite type and Geiss-Leclerc-Schröer's relization of the root system of a symmetrizable Cartan matrix of finite type. This is joint with Ren Wang at USTC.