Gaussian Parts of Compact Quantum Groups

Abstract: We introduce the Gaussian part of a compact quantum group G, namely the largest quantum subgroup of G supporting all the Gaussian functionals of G. We prove that the Gaussian part is always contained in the Kac part, and characterise Gaussian parts of classical compact groups, duals of classical discrete groups and q-deformations of compact Lie groups. The notion turns out to be related to a new concept of "strong connectedness" and we exhibit several examples of both strongly connected and totally strongly disconnected compact quantum groups. Joint work with Amaury Freslon and Adam Skalski.

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.

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