Nakayama automorphisms of graded Ore extensions of Koszul Artin-Schelter regular algebras

TL;DR

This paper characterizes Nakayama automorphisms of graded Ore extensions of Koszul Artin-Schelter regular algebras, introducing the $\sigma$-divergence invariant and explicitly describing automorphisms.

Contribution

It introduces the $\sigma$-divergence invariant for $\sigma$-derivations and explicitly describes Nakayama automorphisms of graded Ore extensions.

Findings

Explicit formula for Nakayama automorphism using $\sigma$-divergence.

Construction of a twisted superpotential for Ore extensions.

Classification of all graded Ore extensions of dimension 2 with their automorphisms.

Abstract

Let $A$ be a Koszul Artin-Schelter regular algebra, $\sigma$ a graded automorphism of $A$ and $\delta$ a degree-one $\sigma$-derivation of $A$. We introduce an invariant for $\delta$ called the $\sigma$-divergence of $\delta$. We describe the Nakayama automorphism of the graded Ore extension $B=A[z;\sigma,\delta]$ explicitly using the $\sigma$-divergence of $\delta$, and construct a twisted superpotential $\hat{\omega}$ for $B$ so that it is a derivation quotient algebra defined by $\hat{\omega}$. We also determine all graded Ore extensions of noetherian Artin-Schelter regular algebras of dimension 2 and compute their Nakayama automorphisms.