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arXiv · 1309.2708

Jacobian algebras with periodic module category and exponential growth

Yadira Valdivieso-Díaz
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Abstract

The Jacobian algebra associated to a triangulation of a closed surface $S$ with a collection of marked points $M$ is (weakly) symmetric and tame. We show that for these algebras the Auslander-Reiten translate acts 2-periodical 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 four properties implies that there is a new family of algebras symmetric, tame and with periodic module category. As a consequence of the 2-periodical actions of the Auslander-Reiten translate on objects, we have that the Auslander-Reiten quiver of the generalized cluster category $\cC_{(S,M)}$ consists only of stable tubes of rank $1$ or $2$.

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BibTeXRIS

Yadira Valdivieso-Díaz. 2016-03-11. Jacobian algebras with periodic module category and exponential growth. https://arxiv.org/abs/1309.2708

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