Nakayama automorphisms of double Ore extensions of Koszul regular algebras

Abstract

Let $A$ be a Koszul Artin-Schelter regular algebra and $\sigma$ an algebra homomorphism from $A$ to $M_{2\times 2}(A)$. We compute the Nakayama automorphisms of a trimmed double Ore extension $A_P[y_1,y_2;\sigma ]$ (introduced in \cite{ZZ08}). Using a similar method, we also obtain the Nakayama automorphism of a skew polynomial extension $A[t;\theta ]$, where $\theta$ is a graded algebra automorphism of $A$. These lead to a characterization of the Calabi-Yau property of $A_P[y_1,y_2;\sigma ]$, the skew Laurent extension $A[t^{\pm 1};\theta ]$ and $A[y_1^{\pm 1},y_2^{\pm 1};\sigma ]$ with $\sigma$ a diagonal type.

The paper has been heavily revised including the title, and will appear in Manuscripta Mathematica