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.

Metadata

Authors/Creators:

Marsh, RJ https://orcid.org/0000-0002-4268-8937
Schroll, S

© 2014, Elsevier. This is an author produced version of a paper accepted for publication in Journal of Algebra. Uploaded in accordance with the publisher's self-archiving policy. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Marsh, RJ and Schroll, S (2014) The geometry of Brauer graph algebras and cluster mutations. Journal of Algebra, 419. 141 - 166.

Keywords:

Special biserial algebras; Brauer graph algebras; Tilting mutation; Derived equivalence; Ribbon graphs; Marked surfaces; Triangulations; Cluster

Dates: