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.