On two-coloured noncrossing partition quantum groups

Abstract

We classify compact quantum groups associated to noncrossing partitions coloured with two elements x x and y y which are their own inverses. Together with the work of P. Tarrago and M. Weber, this completes the classification of all noncrossing partition quantum groups on two colours. We also give some general results on the class of all noncrossing partition quantum groups and suggest some wider classification statements.