Research Projects

The author's research interests lie in Group Theory, specifically the complex projective representations and schur multiplier of finite and infinite groups. The theory of projective representations and schur multiplier has a long history, starting with schur's pioneering works for finite groups. studying projective representations is challenging due to the fact that complex irreducible ordinary representations of abelian groups are one-dimensional. The author plans to study the rational projective representations of abelian groups and nilpotent groups, as projective representations are modules over twisted group algebra. They also plan to study the structure of rational twisted group algebra and find the primitive central idempotent of this group algebra. The ultimate goal is to study the twisted group ring isomorphism problem over rationals, specifically determining the condition under which the groups are isomorphic.