Centers of partly (anti-)commutative quiver algebras and finite generation of the Hochschild cohomology ring
Number of Authors: 2
2016 (English)In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 150, no 3-4, 383-406 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2016. Vol. 150, no 3-4, 383-406 p.
IdentifiersURN: urn:nbn:se:su:diva-132562DOI: 10.1007/s00229-015-0816-9ISI: 000378873600005OAI: oai:DiVA.org:su-132562DiVA: diva2:953606