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.
Nakayama automorphisms play an important role in several mathematical branches, which are known to be tough to compute in general. We compute the Nakayama automorphism ν of any Ore extension R[x; σ, δ] over a polynomial algebra R in n variables for an arbitrary n. The formula of ν is obtained explicitly. When σ is not the identity map, the invariant E G is also investigated in term of Zhang's twist, where G is a cyclic group sharing the same order with σ.
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