Hopf actions and Nakayama automorphisms

TL;DR

This paper explores the relationship between Hopf algebra automorphisms and Nakayama automorphisms in the context of Artin-Schelter regular algebras, providing new insights into their coactions and symmetries.

Contribution

It establishes connections between the Nakayama automorphism of an algebra and the square of the antipode of a Hopf algebra coacting on it, with several applications.

Findings

Relation between Nakayama automorphism and S^2 of Hopf algebra

Characterization of Hopf actions on Artin-Schelter regular algebras

New applications in Hopf algebra symmetries

Abstract

Let H be a Hopf algebra with antipode S, and let A be an N-Koszul Artin-Schelter regular algebra. We study connections between the Nakayama automorphism of A and S^2 of H when H coacts on A inner-faithfully. Several applications pertaining to Hopf actions on Artin-Schelter regular algebras are given.