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Type I locally compact quantum groups: integral characters and coamenability

Volume 561 / 2021

Jacek Krajczok Dissertationes Mathematicae 561 (2021), 1-151 DOI: 10.4064/dm818-9-2020 Published online: 17 May 2021


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.


  • Jacek KrajczokInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland

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