Abstract

We use a tensor C∗-category with conjugates and two quasitensor functors into the category of Hilbert spaces to define a ∗-algebra depending functorially on this data. If one of them is tensorial, we can complete in the maximal C∗-norm. A particular case of this construction allows us to begin with solutions of the conjugate equations and associate ergodic actions of quantum groups on the C∗-algebra in question. The quantum groups involved are Au(Q) and Bu(Q).

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