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Title: Trivial extensions of gentle algebras and Brauer graph algebras
Authors: Schroll, Sibylle
First Published: 27-Aug-2015
Publisher: Elsevier for Academic Press Inc.
Citation: Journal of Algebra, 2015, 444, pp. 183-200
Abstract: We show that two well-studied classes of tame algebras coincide: namely, the class of symmetric special biserial algebras coincides with the class of Brauer graph algebras. We then explore the connection between gentle algebras and symmetric special biserial algebras by explicitly determining the trivial extension of a gentle algebra by its minimal injective co-generator. This is a symmetric special biserial algebra and hence a Brauer graph algebra of which we explicitly give the Brauer graph. We further show that a Brauer graph algebra gives rise, via admissible cuts, to many gentle algebras and that the trivial extension of a gentle algebra obtained via an admissible cut is the original Brauer graph algebra.As a consequence we prove that the trivial extension of a Jacobian algebra of an ideal triangulation of a Riemann surface with marked points in the boundary is isomorphic to the Brauer graph algebra with Brauer graph given by the arcs of the triangulation.
DOI Link: 10.1016/j.jalgebra.2015.07.037
ISSN: 0021-8693
eISSN: 1090-266X
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2015 Elsevier Inc. All rights reserved. Deposited with reference to the publisher’s archiving policy available on the SHERPA/RoMEO website.
Appears in Collections:Published Articles, Dept. of Mathematics

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