Reflexive hull discriminants and applications

Abstract: In algebraic number theory, the discriminant is an important invariant of a Galois field extension. There is a notion of the discriminant for noncommutative algebras that are finite modules over their centers. This has been used to solve several challenging problems, such as to classify the automorphism groups of certain families of noncommutative algebras. But the discriminant is notoriously difficult to compute in large rank. In this talk, I will review some of the history behind the discriminant invariant and introduce a new notion, the reflexive hull discriminant. This modification has a geometric interpretation and, moreover, is well-suited for algebras that are finitely generated but not necessarily free over their centers. As an application, I will show how this invariant can be used to determine the automorphism groups for certain quantum generalized Weyl algebras.

rings and algebrasrepresentation theory

Audience: researchers in the topic

ONCAS Online Noncommutative Algebra Seminar

Series comments: This is an online seminar organized to keep the community of noncommutative algebraists connected during the pandemic which has made it difficult for everyone to travel. If you would like to attend these talks, please email to any of the organizers and you will be added to the mailing list.