Connectedness and Gaussian Parts for Compact Quantum Groups

Abstract

We introduce the Gaussian part of a compact quantum group $\mathbb{G}$, namely the largest quantum subgroup of $\mathbb{G}$ supporting all the Gaussian functionals of $\mathbb{G}$. 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.

23 pages; v3 changes the title

References in corpus (1)

• A Characterization of right coideals of quotient type and its application to classification of Poisson boundaries

Cited by in corpus (1)

• Gaussian Generating functionals on easy quantum groups