Twisted Calabi–Yau property of Ore extensions

Abstract

Suppose that $E=A[x;\sigma,\delta]$ is an Ore extension with $\sigma$ an automorphism. It is proved that if $A$ is twisted Calabi–Yau of dimension $d$, then $E$ is twisted Calabi–Yau of dimension $d+1$. The relation between their Nakayama automorphisms is also studied. As an application, the Nakayama automorphisms of a class of 5-dimensional Artin–Schelter regular algebras are given explicitly.