Abstract:
In this article, we study homogeneous spacesUq(2)/φTandUq(2)/ψTof the compactquantum groupUq(2),q∈C\{0}. The homogeneous spaceUq(2)/φTis shown to bethe braided quantum groupSUq(2). The homogeneous spaceUq(2)/ψTis establishedas a universalC∗-algebra given by a finite set of generators and relations. ItsK-groupsare computed and two families of finitely summable odd spectral triples, one isUq(2)-equivariant and the other isT2-equivariant, are constructed. Using the index pairing,it is shown that the induced Fredholm modules for these families of spectral triplesgive each element in theK-homology groupK1(C(Uq(2)/ψT)).