Degree bounds for Hopf actions on Artin-Schelter regular algebras

TL;DR

This paper investigates how semisimple Hopf algebra actions influence the structure of Artin-Schelter regular algebras, establishing bounds on the degrees of generators and syzygies of invariant subrings, extending classical results from commutative polynomial rings.

Contribution

It provides new degree bounds for invariants under Hopf actions on noncommutative regular algebras, generalizing classical invariant theory results.

Findings

Upper bounds on degrees of minimal generators

Bounds on degrees of syzygies

Analogues of classical invariant theory results

Abstract

We study semisimple Hopf algebra actions on Artin-Schelter regular algebras and prove several upper bounds on the degrees of the minimal generators of the invariant subring, and on the degrees of syzygies of modules over the invariant subring. These results are analogues of results for group actions on commutative polynomial rings proved by Noether, Fogarty, Fleischmann, Derksen, Sidman, Chardin, and Symonds.