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arXiv · 1606.02071

Monoidal category of C*-algebras

S. L. Woronowicz
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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.

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S. L. Woronowicz. 2016-06-07. Monoidal category of C*-algebras. https://arxiv.org/abs/1606.02071

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