Zestings for Hopf algebras

Abstract: In this talk, I will present a framework for "zestings" of Hopf algebras, a technique we hve extended from fusion categories to general tensor categories. I will provide a detailed translation of the categorical zesting construction into explicit Hopf algebraic terms. We show how associative zesting of a Hopf algebra's comodule category yields a coquasi-Hopf algebra, where the comodule category of this new structure is precisely the zested category.

Furthermore, we present concrete formulas for constructing zestings of pointed Hopf algebras, particularly for cyclic group gradings, encompassing both diagonal and non-diagonal braided vector spaces. Finally, I will illustrate this construction with new examples of coquasi-Hopf algebras, including those derived from Nichols algebras of super type A(1|2) and the Fomin-Kirillov algebra in three variables.

This is joint work with Ivan Angiono and Giovanny Mora.

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