Nakayama automorphisms of Ore extensions over polynomial algebras

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 $\nu$ of any Ore extension $R[x; \sigma, \delta]$ over a polynomial algebra $R$ in $n$ variables for an arbitrary $n$. The formula of $\nu$ is obtained explicitly. When $\sigma$ 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 $\sigma$.