Modular invariants of quantum groups

Abstract: A very interesting feature of compact quantum groups is that their Haar integral, which is a normal state on $L^{\infty}(G)$, can be non-tracial. Via Tomita-Takesaki theory, this gives rise to two groups of automorphisms: modular automorphisms and scaling automorphisms. One can use them to define a number of invariants, related to whether these automorphisms are trivial, inner or approximately inner. During the talk I'll introduce such invariants (also in the general locally compact case), discuss a conjecture related to one of them, and present their calculation in the case of q-deformed compact, simply connected, semisimple Lie group $G_q$. The talk is based on a joint work with Piotr Sołtan.

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.