C* 代数的幺半范畴

摘要：

本文研究了具有局部紧量子群作用的C* 代数-代数范畴。我们证明了这个范畴允许一个满足一定自然条件的么半群结构当且仅当这个群是拟三角群。monoidal结构与酉R矩阵具有双射对应。为了证明这一结果，我们只使用非常自然的性质强加于所考虑的monoidal结构。我们假设Monoidal积是交叉积，单射态射的Monoidal积是单射的，并且当其中一个C* 代数-代数具有群的平凡作用时，Monoidal积约化为极小张量积.没有使用monoidal乘积的先验形式。

英文摘要：

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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