Maity, Kiran2026-02-102026-02-102026-01-22115p.http://hdl.handle.net/10263/7649This thesis is under the supervision of Dr. Debashish GoswamiIn this thesis, we briefly review various types of projective corepresentations of compact quantum groups and prove the existence of suitable envelopes for them. We also study the associated invariant (dual) 2-cohomology and calculate it in a few concrete examples.en20G42, 18M15, 18M20Thesis