Discriminants of Taft algebra smash products and applications

TL;DR

This paper establishes criteria for the center of Taft algebra smash products, computes their discriminants, and explores applications to Azumaya loci and automorphism groups using Poisson methods.

Contribution

It introduces a general criterion for centers of Taft algebra smash products and fully determines actions on quantum algebras, applying Poisson techniques.

Findings

Criteria for centers of smash products established

Discriminants of specific smash products computed

Applications to Azumaya loci and automorphism groups demonstrated

Abstract

A general criterion is given for when the center of a Taft algebra smash product is the fixed ring. This is applied to the study of the noncommutative discriminant. Our method relies on the Poisson methods of Nguyen, Trampel, and Yakimov, but also makes use of Poisson Ore extensions. Specifically, we fully determine the inner faithful actions of Taft algebras on quantum planes and quantum Weyl algebras. We compute the discriminant of the corresponding smash product and apply it to compute the Azumaya locus and restricted automorphism group.