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

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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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Authors and Affiliations

  1. Stockholms Universitet, Stockholm, Sweden

    Elin Gawell & Qimh Richey Xantcha

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  1. Elin Gawell
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  2. Qimh Richey Xantcha
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Correspondence to Elin Gawell.

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Gawell, E., Xantcha, Q.R. Centers of partly (anti-)commutative quiver algebras and finite generation of the Hochschild cohomology ring. manuscripta math. 150, 383–406 (2016). https://doi.org/10.1007/s00229-015-0816-9

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  • DOI: https://doi.org/10.1007/s00229-015-0816-9

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