Hopf actions on filtered regular algebras

TL;DR

This paper investigates finite dimensional Hopf algebra actions on filtered Artin-Schelter regular algebras of dimension 2, analyzing their properties and the structure of fixed subrings, with implications for algebraic regularity and Gorenstein conditions.

Contribution

It provides new insights into Hopf actions on filtered regular algebras, especially regarding Gorenstein conditions and fixed subring properties in dimension 2.

Findings

Finite dimensional Hopf actions on filtered Artin-Schelter regular algebras are characterized.

Results on Gorenstein conditions for fixed subrings are established.

Global dimension properties of fixed subrings are analyzed.

Abstract

We study finite dimensional Hopf algebra actions on so-called filtered Artin-Schelter regular algebras of dimension n, particularly on those of dimension 2. The first Weyl algebra is an example of such on algebra with n=2, for instance. Results on the Gorenstein condition and on the global dimension of the corresponding fixed subrings are also provided.