Algebra and Geometry Seminar
In this talk I will give an overview of symmetric tensor categories, with a focus on the Verlinde category, a universal base for semisimple symmetric tensor categories in positive characteristic. I will give an explicit construction of the Verlinde category, describe its fusion rules and motivate its study via some representation theoretic constructions. In particular, I will describe an elementary construction in the Verlinde category that gives us examples of exceptional Lie superalgeras in charactetistic p.
Subsequently, I will describe the algebro-geometric properties of finitely generated commutative rings in the Verlinde category, with an emphasis on describing the Frobenius images of simple summands of these rings, and then use this to construct a correspondence between affine group schemes in this category and Harish-Chandra pairs, i.e., pairs of ordinary affine group schemes and Lie algebras in the Verlinde category with compatible adjoint actions.