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Title: Jacobian algebras with periodic module category and exponential growth
Authors: Valdivieso-Díaz, Yadira
First Published: 14-Nov-2015
Publisher: Elsevier for Academic Press
Citation: Journal of Algebra, 2016, 449, pp. 163-174
Abstract: Recently it was proven by Geiss, Labardini-Fragoso and Sh¨oer in [1] that every Jacobian algebra associated to a triangulation of a closed surface S with a collection of marked points M is tame and Ladkani proved in [2] these algebras are (weakly) symmetric. In this work we show that for these algebras the Auslander-Reiten translation acts 2-periodically on objects. Moreover, we show that excluding only the case of a sphere with 4 (or less) punctures, these algebras are of exponential growth. These results imply that the existing characterization of symmetric tame algebras whose non-projective indecomposable modules are Ω-periodic, has at least a missing class (see [3, Theorem 6.2] or [4]). As a consequence of the 2-periodical actions of the Auslander-Reiten translation on objects, we have that the Auslander-Reiten quiver of the generalized cluster category C(S,M) consists only of stable tubes of rank 1 or 2.
DOI Link: 10.1016/j.jalgebra.2015.09.051
ISSN: 0021-8693
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © Elsevier for Academic Press 2015. This version of the paper is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License (, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Appears in Collections:Published Articles, Dept. of Mathematics

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