Bijections of silting complexes and derived Picard groups

Abstract: I will start with an introduction to derived categories and derived equivalences of finite-dimensional algebras, and the notion of silting complexes. I will then talk about results on two large classes of finite-dimensional algebras, namely Brauer graph algebras and the weighted surface algebras introduced by Erdmann and Skowronski, which show that these algebras have multiplicity-independent sets of silting complexes. The key ingredient for this is the existence of lifts of these algebras to orders over formal power series rings, which are remarkably similar to orders over p-adic rings encountered in the modular representation theory of finite groups.

Mathematics

Audience: researchers in the topic

Greek Algebra & Number Theory Seminar