A Theory of Locally Convex Hopf Algbebras -- II. More Duality Results and Examples

Abstract: This is the second of two talks on a recent theory of locally convex Hopf algebras. We will start by presenting a generalized version of the Gelfand duality, and later apply it in various situations to obtain the underlying topological group from the corresponding locally convex Hopf algebras. Surprisingly, we can go much beyond the locally compact case in this classical situation, and make the theory work for all topological groups with compactly generated topology. Then we shift to some categorical considerations, allowing us to obtain new topological quantum groups as well as their dualities that seem not in the locally compact framework of Kustermans-Vaes. If time permits, we will conclude by mentionning how some deep structural results related to Hilbert's fifth problem can be applied in this theory.

operator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

The zoom links will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.