The geometry of Brauer graph algebras and cluster mutations

2013/09/17 by Bethany Marsh, Sibylle Schroll, Marsh, Bethany +1
Mathematics · #14J10 #16E35 #16G20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary: 16G10 #Representation Theory (math.RT) #Secondary: 13F160

paper · pdf · doi:10.48550/arxiv.1309.4239

openalex publication_date 2013/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Quivers with potentials and their representations I: Mutations
• Trivial Extensions of Gentle Algebras and Brauer Graph Algebras
• Defining an m-cluster category

Related

• Brauer graph algebras
• Mutation of Brauer configuration algebras
• Tilting mutations as generalized Kauer moves for (skew) Brauer graph algebras with multiplicity
• Mutations and Pointing for Brauer Tree Algebras
• Generalized Kauer moves and derived equivalences of Brauer graph algebras