Is there any description (preferably somehow related to the original generators) for the state space (as in C*-algebras) of quantum SU(2) and the Podleś sphere? If so (this is pushing my luck) are the extremal states known?
I know that using the Haar integral lots of normalised states can be written as $\phi(a)=\int(b\,a\,b^*)/\int(b\,b^*)$. However this may not be the most useful description, and will probably only get a dense subset at best. Most importantly, it doesn't really say much (that I know of) about the extremal states.
The reason for the question? Trying to relate the differential geometry (Woronowicz et al) of these spaces to the C* structure in some `easy' (??) cases, in the hope that it can be generalised.
