Classification of graded Hopf algebra quotients

Abstract: Let $G$ be a group. A Hopf algebra $H$ is called $G$-graded if $H$ is $G$-graded as an algebra, and the grading is compatible with the comultiplication, counit and antipode. Examples of such Hopf algebras include cocentral extensions of Hopf algebras and the twisted Drinfeld double of groups. In this talk, we present a classification of Hopf ideals for a $G$-graded (quasi-)Hopf algebra based on the following parametrization: normal subgroups $N$ of $G$, Hopf ideals in the homogeneous component of the identity $H_e$ that are invariant under $N$, and $G$-equivariant trivializations of a specific quotient constructed with these parameters. This approach incorporates ideas from earlier work by César Galindo and Corey Jones, who parameterized all fusion subcategories arising from equivariantization through a group action on a fusion category. However, in our results, the Hopf algebras are not necessarily semisimple, and $G$ is not necessarily finite. This talk is based on ongoing joint work with César Galindo.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home