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Title: The geometry of Brauer graph algebras and cluster mutations
Authors: Marsh, Robert J.
Schroll, Sibylle
First Published: 25-Aug-2014
Publisher: Elsevier for Academic Press
Citation: Journal of Algebra, 2014, 419, pp. 141-166 (26)
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.
DOI Link: 10.1016/j.jalgebra.2014.08.002
ISSN: 0021-8693
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Archived with reference to SHERPA/RoMEO and publisher website. 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 Journal of Algebra, 419 (2014) DOI 10.1016/j.jalgebra.2014.08.002
Description: MSC primary, 16G10, 16G20, 16E35; secondary, 13F60, 14J10
Appears in Collections:Published Articles, Dept. of Mathematics

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