Derived equivalence classification of Brauer graph algebras

Alexandra Zvonareva (University of Stuttgart)

Wednesday 24th April 16:00-17:00 Maths 311B

Abstract

This talk is based on work in progress, joint with Mikhail Antipov and 
with Sebastian Opper.

Brauer graph algebras or equivalently symmetric special biserial 
algebras originate in modular representation theory and are studied quit 
well. In the talk I will concentrate on two results: the fact that 
Brauer graph algebras are closed under derived equivalence and a 
complete classification of Brauer graph algebras up to derived 
equivalence. For the second result we use the classification of gentle 
algebras up to derived equivalence obtained by Lekili, Polishchuk; 
Opper; Amiot, Plamondon and Schroll as well as  combinatorial derived 
invariants of Brauer graph algebras introduced by Antipov and some 
general techniques used to study derive equivalences, such as trivial 
extensions and coverings.

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