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We use a tensor C*-category with conjugates and two quasitensor functors intothe category of Hilbert spaces to define a *-algebra depending functorially onthis 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 theconjugate equations and associate ergodic actions of quantum groups on theC*-algebra in question. The quantum groups involved are A_u(Q) and B_u(Q).

Ergodic actions of compact quantum groups from solutions of the conjugate equations