Reflexive hull discriminants and applications

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.