The geometry of Brauer graph algebras and cluster mutations

Bethany Marsh; Sibylle Schroll

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arXiv · 1309.4239

The geometry of Brauer graph algebras and cluster mutations

Bethany Marsh·Sibylle Schroll

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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.

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Bethany Marsh, Sibylle Schroll. 2013-09-17. The geometry of Brauer graph algebras and cluster mutations. https://arxiv.org/abs/1309.4239

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