1309.4239v2.pdf (320.59 kB)
The geometry of Brauer graph algebras and cluster mutations
journal contributionposted on 2015-03-09, 09:51 authored by Robert J. Marsh, Sibylle Schroll
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.
CitationJournal of Algebra, 2014, 419, pp. 141-166 (26)
Author affiliation/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics
- AM (Accepted Manuscript)