Suppose that E = A[x; σ, δ] is an Ore extension with σ 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.
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