A Theory of Locally Convex Hopf Algebras -- I. Basic Theory and Examples

Abstract: This is the first of two talks on a recent theory of locally convex Hopf algebras. After a brief introduction to some relevant facts on locally convex spaces as well as their topological tensor products, we will describe the main theory with an emphasis on duality. We will see that besides the usual strong dual, the theory encompasses naturally a new type of dual called the polar dual. After presenting the main theoretical results, we will illustrate the theory with various examples. In particular, we will see how to resolve the duality problem for classical Hopf algebras, how to describe a Lie group as well as its dual using smooth functions, and how to incorporate compact and discrete quantum groups into this framework.

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.