Note on Nakayama automorphisms of PBW deformations and Hopf actions

TL;DR

This paper explores the Nakayama automorphisms of PBW deformations of Artin-Schelter regular algebras, linking their properties to homogenizations and Hopf actions, and generalizes Calabi-Yau properties beyond Koszul cases.

Contribution

It demonstrates how Nakayama automorphisms of PBW deformations can be derived from homogenizations and relates these automorphisms to Hopf actions, extending Calabi-Yau properties.

Findings

Nakayama automorphisms derived from homogenizations

Calabi-Yau properties extended beyond Koszul assumptions

Nakayama automorphisms control Hopf actions

Abstract

PBW deformations of Artin-Schelter regular algebras are skew Calabi-Yau. We prove that the Nakayama automorphisms of such PBW deformations can be obtained from their homogenizations. Some Calabi-Yau properties are generalized without Koszul assumption. We also show that the Nakayama automorphisms of such PBW deformations control Hopf actions on them.