LAUSR

AbstractWe use a tensor C ∗ –category with conjugates and two quasitensor func-tors into the category of Hilbert spaces to define a C ∗ –algebra dependingfunctorially on this data. A particular case of this construction allows usto begin with solutions of the conjugate equations and associate ergodicactions of quantum groups on the C ∗ –algebra in question. The quantumgroups involved are A u (Q) and B u (Q). 1 2 1 Introduction The theory of ergodic actions of compact quantum groups on unital C ∗ –algebrashas recently attracted interest. In the group case, one of the first results was thetheorem by Hoegh-Krohn, Landstad and Stormer asserting that the multiplicityof an irreducible representation is always bounded by its dimension and thatthe unique G–invariant state is a trace [9].Ergodic theory for group actions was later investigated by Wassermann in aseries of papers [19], [20], [21], who, among other results, classified all ergodicactions of SU(2) on von Neumann algebras. In particular, he proved the im-portant result that SU(2) cannot act ergodically on the hyperfinite II