Nakayama automorphisms of Ore extensions over polynomial algebras
Liyu Liu, Wen Ma

TL;DR
This paper provides an explicit formula for Nakayama automorphisms of Ore extensions over polynomial algebras, extending understanding of their structure and invariants in algebraic contexts.
Contribution
It explicitly computes Nakayama automorphisms for Ore extensions over polynomial algebras, including cases where the automorphism is nontrivial.
Findings
Explicit formula for Nakayama automorphism $ u$ of Ore extensions.
Analysis of invariant $E^G$ via Zhang's twist when $\sigma$ is not identity.
Extension of automorphism computation to arbitrary $n$ variables.
Abstract
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 of any Ore extension over a polynomial algebra in variables for an arbitrary . The formula of is obtained explicitly. When is not the identity map, the invariant is also investigated in term of Zhang's twist, where is a cyclic group sharing the same order with .
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