# Algebra and Geometry Seminar: Twisting of function algebras on algebraic groups

**Author: Lona**

**Author: Lona**

Speaker: Shlomo Gelaki (ISU)

Abstract: Fix a complex linear algebraic group G. Let O(G) denote the function algebra of G (it is a commutative Hopf algebra), and let Rep(G) denote the representation category of G (it is a symmetric tensor category). In my talk I will first explain why (ordinary) fiber functors F:Rep(G)→Vect correspond to Drinfeld twistings J of O(G), namely to twisting Hopf algebras O(G)J, and then focus on the algebra structure and representation theory of the (not necessarily commutative) Hopf algebras O(G)J and the one-sided twisted algebras O(G)J for nilpotent G. Finally, I will discuss some open problems and conjectures for arbitrary G (e.g., solvable, reductive).