Fusion (semi)rings arising from quantum groups
Quantum Algebra
2017-09-20 v3 Operator Algebras
Representation Theory
Abstract
We study the fusion semirings arising from easy quantum groups. We classify all the possible free ones, answering a question of T. Banica and R. Vergnioux : these are exactly the fusion rings of quantum groups without any nontrivial one-dimensional representation. We then classify the possible groups of one-dimensional representations for free easy quantum groups. As an application, we give a unified proof of the Haagerup property for a broad class of easy quantum groups, recovering as special cases previous results by M. Brannan and F. Lemeux. We end with some considerations on the description of the full fusion ring in the general case.
Keywords
Cite
@article{arxiv.1311.0782,
title = {Fusion (semi)rings arising from quantum groups},
author = {Amaury Freslon},
journal= {arXiv preprint arXiv:1311.0782},
year = {2017}
}
Comments
35 pages. A flaw in the statement and proof of Thm 6.11 has been corrected