The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Journal of Noncommutative Geometry

Full-Text PDF (328 KB) | Metadata | Table of Contents | JNCG summary
Volume 13, Issue 1, 2019, pp. 35–58
DOI: 10.4171/JNCG/322

Published online: 2019-03-11

Torsion-freeness for fusion rings and tensor C*-categories

Yuki Arano[1] and Kenny De Commer[2]

(1) Kyoto University, Japan
(2) Vrije Universiteit Brussel, Brussels, Belgium

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: Quantum groups, tensor categories, free quantum groups, fusion rings

Arano Yuki, De Commer Kenny: Torsion-freeness for fusion rings and tensor C*-categories. J. Noncommut. Geom. 13 (2019), 35-58. doi: 10.4171/JNCG/322