Cohomology of free unitary quantum groups

Abstract: In the talk, we will discuss the free unitary quantum groups (or "universal quantum groups") of Wang and van Daele from a (co)homological perspective. We find a free resolution of the counit, a versatile tool which helps to compute cohomological data such as Hochschild cohomology or bialgebra cohomology of the associated Hopf algebras. For free orthogonal quantum groups, such resolutions have been found by Collins, Härtel, and Thom (in the Kac-case) and Bichon (in the general case), and they will serve as our starting point for finding resolutions for free unitary quantum groups.

Based on joint work with I. Baraquin, U. Franz, A. Kula and M. Tobolski [arXiv:2309.07767]

category theoryoperator 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.