Monoidal category of C*-algebras
Operator Algebras
2016-06-08 v1 Functional Analysis
Abstract
We consider the category of C*-algebras equipped with actions of a locally compact quantum group. We show that this category admits a monoidal structure satisfying certain natural conditions if and only if the group is quasitriangular. The monoidal structures are in bijective correspondence with unitary R-matrices. To prove this result we use only very natural properties imposed on considered monoidal structures. We assume that monoidal product is a crossed product, monoidal product of injective morphisms is injective and that monoidal product reduces to the minimal tensor product when one of the involved C*-algebras is equipped with a trivial action of the group. No a priori form of monoidal product is used.
Keywords
Cite
@article{arxiv.1606.02071,
title = {Monoidal category of C*-algebras},
author = {S. L. Woronowicz},
journal= {arXiv preprint arXiv:1606.02071},
year = {2016}
}