  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.
