Important families of noncommutative algebras turn out to be Cayley-Hamilton Hopf algebras including finitely generated group algebras with large center and quantum groups at roots of unity. Discriminants and discriminant ideals are important invariants that are related to automorphisms and representations of noncommutative algebras. We study the zero set of the lowest discriminant ideal of Cayley-Hamilton Hopf algebras using the tensor categorical structure of their representations.

This is joint work with Yimin Huang, Tiancheng Qi, Quanshui Wu and Milen Yakimov.