Torsion-freeness for fusion rings and tensor C*-categories
Abstract
Torsion-freeness for discrete quantum groups was introduced by R. Meyer in order to formulate a version of the Baum-Connes conjecture for discrete quantum groups. In this note, we introduce torsion-freeness for abstract fusion rings. We show that a discrete quantum group is torsion-free if its associated fusion ring is torsion-free. In the latter case, we say that the discrete quantum group is strongly torsion-free. As applications, we show that the discrete quantum group duals of the free unitary quantum groups are strongly torsion-free, and that torsion-freeness of discrete quantum groups is preserved under Cartesian and free products. We also discuss torsion-freeness in the more general setting of abstract rigid tensor C*-categories
Keywords
Cite
@article{arxiv.1511.07982,
title = {Torsion-freeness for fusion rings and tensor C*-categories},
author = {Yuki Arano and Kenny De Commer},
journal= {arXiv preprint arXiv:1511.07982},
year = {2015}
}
Comments
29 pages; Remark 3.13 has been corrected and made into two seperate comments (Remarks 3.13 and 3.15)