The geometry of Brauer graph algebras and cluster mutations

Abstract

In this paper we establish a connection between ribbon graphs and Brauer graphs. As a result, we show that a compact oriented surface with marked points gives rise to a unique Brauer graph algebra up to derived equivalence. In the case of a disc with marked points we show that a dual construction in terms of dual graphs exists. The rotation of a diagonal in an m-angulation gives rise to a Whitehead move in the dual graph, and we explicitly construct a tilting complex on the related Brauer graph algebras reflecting this geometrical move.

19 pages, 14 figures. Minor changes only

References in corpus (4)

• Dimer models and cluster categories of Grassmannians
• Ice quivers with potentials associated with triangulations and Cohen-Macaulay modules over orders
• Defining an m-cluster category
• Trivial Extensions of Gentle Algebras and Brauer Graph Algebras

Cited by in corpus (3)

• Algebras of quasi-quaternion type
• On the derived Picard group of the Brauer star algebra
• Derived equivalences between symmetric special biserial algebras