The purpose of my talk is to discuss the following results recently obtained in collaboration with A.Masuoka (Tsukuba University, Japan). First, we prove that a certain category of Harish-Chandra pairs is equivalent to the category of (not necessary affine) locally algebraic group superschemes. Using this fundamental equivalence we superize the famous Barsotti-Chevalley theorem and prove that the sheaf quotient of an algebraic group superscheme over its group super-subscheme is again a superscheme of finite type. I will also formulate some open problems whose solving would bring significant progress in the supergroup theory.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
