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arXiv · 1504.00582

Centers of partly (anti-)commutative quiver algebras and finite generation of the Hochschild cohomology ring

Elin Gawell·Qimh Richey Xantcha
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Abstract

A partly (anti-)commutative quiver algebra is a quiver algebra bound by an (anti-)commutativity ideal, that is, a quadratic ideal generated by monomials and (anti-)commutativity relations. We give a combinatorial description of the ideals and the associated generator graphs, from which one can quickly determine if the ideal is admissible or not. We describe the center of a partly (anti-)commutative quiver algebra and state necessary and sufficient conditions for the center to be finitely generated as a K-algebra. As an application, necessary and sufficient conditions for finite generation of the Hochschild cohomology ring modulo nilpotent elements for a partly (anti-)commutative Koszul quiver algebra are given.

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Elin Gawell, Qimh Richey Xantcha. 2015-04-02. Centers of partly (anti-)commutative quiver algebras and finite generation of the Hochschild cohomology ring. https://arxiv.org/abs/1504.00582

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