Nakayama automorphism of quasi-commutative skew PBW extensions over AS-regular algebras

TL;DR

This paper studies Nakayama automorphisms of graded quasi-commutative skew PBW extensions over AS-regular algebras, showing they are skew Calabi-Yau and describing their automorphisms based on the coefficient ring.

Contribution

It provides a description of Nakayama automorphisms for these extensions, linking them to the automorphisms of the coefficient ring, and establishes their skew Calabi-Yau property.

Findings

Extensions are isomorphic to graded iterated Ore extensions.

Extensions with coefficients in AS-regular algebras are skew Calabi-Yau.

Nakayama automorphism is described via the coefficient ring's automorphism.

Abstract

Graded quasi-commutative skew PBW extensions are isomorphic to graded iterated Ore extensions of endomorphism type, whence graded quasi-commutative skew PBW extensions with coefficients in AS-regular algebras are skew Calabi-Yau and the Nakayama automorphism exists for these extensions. With this in mind, in this paper we give a description of Nakayama automorphism for these non-commutative algebras using the Nakayama automorphism of the ring of the coefficients.