NEW PRODUCTS AND Z(2)-EXTENSIONS OF COMPACT MATRIX QUANTUM GROUPS

There are two very natural products of compact matrix quantum groups: the tensor product G x H and the free product G * H. We define a number of further products interpolating these two. We focus more in detail to the case where G is an easy quantum group and H = (Z) over cap (2), the dual of the cyclic group of order two. We study subgroups of G * (Z) over cap (2) using categories of partitions with extra singletons. Closely related are many examples of non-easy bistochastic quantum groups.