# Wydawnictwa / Czasopisma IMPAN / Dissertationes Mathematicae / Artykuły Online First

## Type I locally compact quantum groups: integral characters and coamenability

Dissertationes Mathematicae (2021) DOI: 10.4064/dm818-9-2020 Opublikowany online: 17 May 2021

#### Streszczenie

We establish two conditions equivalent to coamenability for type I locally compact quantum groups. The first condition is related to the spectra of certain convolution operators on the space $\operatorname{L}^2(\operatorname{Irr}\mathbb G)$ of functions square integrable with respect to the Plancherel measure. The second condition involves spectra of character-like operators (called integral characters) associated with direct integrals of irreducible representations. These two conditions are closely related: we prove that convolution operators are unitarily equivalent to integral characters. As examples we study special classes of quantum groups: classical, dual to classical, compact, and given by a certain bicrossed product construction.

#### Autorzy

• Jacek KrajczokInstitute of Mathematics