Valentine Soto (Université Grenoble Alpes) – Generalized Kauer moves and derived equivalences of skew Brauer graph algebras

Brauer graph algeras are finite dimensional algebras constructed from the combinatorial data of a graph called a Brauer graph. Kauer proved that derived equivalences of Brauer graph algebras can be obtained from the move of one edge in the corresponding Brauer graph. Moreover, this derived equivalence is entirely described thanks to a tilting object which can be interpreted in terms of silting mutation. In this talk, I will be interested in skew Brauer graph algebras which generalize the class of Brauer graph algebras. These algebras are constructed from the combinatorial data of a Brauer graph where some edges might be "degenerate". I will explain how Kauer's results can be generalized for the move of multiple edges and to the case of skew Brauer graph algebras.