Compact quantum groups with representations of bounded degree
Quantum Algebra
2017-10-16 v1 Functional Analysis
Operator Algebras
Abstract
We show that a compact quantum group all whose 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 spectrum of these operators and the dimension of some of their eigenspaces in relation to the quantum dimension of the corresponding irreducible representation.
Cite
@article{arxiv.1710.04863,
title = {Compact quantum groups with representations of bounded degree},
author = {Jacek Krajczok and Piotr M. Sołtan},
journal= {arXiv preprint arXiv:1710.04863},
year = {2017}
}
Comments
17 pages