Classification, Koszulity and Artin-Schelter Regularity of certain Graded Twisted Tensor Products

Abstract

Let $\mathbb{k}$ be an algebraically closed field. We classify all of the quadratic twisted tensor products $A{\otimes }_{\tau }B$ in the cases where $(A,B)=(\mathbb{k}[x],\mathbb{k}[y])$ and $(A,B)=(\mathbb{k}[x,y],\mathbb{k}[z])$. We determine when a quadratic twisted tensor product of this form is Koszul, and when it is Artin-Schelter regular.

31 pages; version 2: minor change to title, minor copy-edits based on referee report, to appear in The Journal of Noncommutative Geometry