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The geometry of Brauer graph algebras and cluster mutations
journal contribution
posted on 2015-03-09, 09:51 authored by Robert J. Marsh, Sibylle SchrollIn 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.
History
Citation
Journal of Algebra, 2014, 419, pp. 141-166 (26)Author affiliation
/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of MathematicsVersion
- AM (Accepted Manuscript)