Cocycle twists of tensor categories and of rational Cherednik algebras

24 January 2013
14:00
Yuri Bazlov
Abstract
Central extensions of a finite group G correspond to 2-cocycles on G, which give rise to an abelian cohomology group known as the Schur multiplier of G. Recently, the Schur multiplier was defined in a much more general setting of a monoidal category. I will explain how to twist algebras by categorical 2-cocycles and will mention the role of such twists the theory of quantum groups. I will then describe an approach to twisting rational Cherednik algebras by cocycles, and will discuss possible applications of this new construction to the representation theory of these algebras.
  • Representation Theory Seminar