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

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