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 classifies projective representations? The problem I am working on hints me to investigate this question. So I’m naturally interested in the analog of continuous/Borel/Eilenberg-Moore (I’ve heard all these phrases being used) cohomology developed for compact topological (Lie) in the quantum setting. 

Borel cohomology: [See this paper][1]


  [1]: https://projecteuclid.org/journalArticle/Download?urlId=bams%2F1183540920