We use a tensor -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 -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 -algebra in question. The quantum groups involved are and .
"Ergodic actions of compact quantum groups from solutions of the conjugate equations." Kyoto J. Math. 57 (3) 519 - 552, September 2017. https://doi.org/10.1215/21562261-2017-0005