I'm interested in quantum groups for two perspectives:

 1. Compact quantum groups in the sense of Woronowicz.
 2. Deformation of the universal enveloping algebra of a Lie algebra in the sense of Drinfeld \& Jimbo.

I'm intetsed in knowing about what cohomology theories are out there for quantum groups from these perspectives. I would appreciate pointers to some references.

**Edit:** To elaborate on the question: is there a cohomology theory associated with groups such as $SO_q(n), SU_q(n)$ - essentially quantum analogs of classical compact Lie groups - in which the second cohomology group, $H^2$, classifies projective representations? This would parallel the classification of projective representations for both finite groups and classical Lie groups.