Journal of Operator Theory

Volume 80, Issue 2, Fall 2018 pp. 415-428.

Compact quantum groups with representations of bounded degree

Authors: Jacek Krajczok (1) and Piotr M. Soltan (2)
Author institution: (1) Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Poland
(2) Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Poland

Summary: We show that a compact quantum group whose all irreducible representations have dimension bounded by a fixed constant must be of Kac type, in other words, its Haar measure is a trace. The proof is based on establishing several facts concerning operators related to modular properties of the Haar measure. In particular we study the spectrum of these operators and the dimensions of some of their eigenspaces in relation to the quantum dimension of the corresponding irreducible representation.

DOI: http://dx.doi.org/10.7900/jot.2017oct23.2181
Keywords: compact quantum group, representation, dimension, quantum dimension

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