Reflexive hull discriminants and applications

TL;DR

This paper introduces reflexive hull discriminants as a new tool for analyzing noncommutative algebras, enabling the computation of automorphism groups and other properties, with applications to quantum generalized Weyl algebras.

Contribution

It defines reflexive hull discriminants and demonstrates their use in studying automorphisms of noncommutative algebras, extending previous results.

Findings

Computed reflexive hull discriminants for quantum generalized Weyl algebras

Determined automorphism groups using these discriminants

Recovered known results in the literature

Abstract

We introduce the reflexive hull discriminant as a tool to study noncommutative algebras that are finitely generated, but not necessarily free, over their centers. As an example, we compute the reflexive hull discriminants for quantum generalized Weyl algebras and use them to determine automorphism groups and other properties, recovering results of Su{\'a}rez-Alvarez, Vivas, and others.