Generalized Kauer moves and derived equivalences of Brauer graph algebras

Abstract

Kauer moves are local moves of an edge in a Brauer graph that yield derived equivalences between Brauer graph algebras [Kau98]. These derived equivalences may be interpreted in terms of silting mutations. In this paper, we generalize the notion of Kauer moves to any finite number of edges. Their construction is based on cutting and pasting actions on the Brauer graph. To define these actions, we use an alternative definition of Brauer graphs coming from combinatorial topology [Laz14]. Using the link between Brauer graph algebras and gentle algebras via the trivial extension [Sch15], we show that the generalized Kauer moves also yield derived equivalences of Brauer graph algebras and also may be interpreted in terms of silting mutations.