The study of symmetric categories over fields of positive characteristic has gained a lot of attention in the last couple of years. One of the key examples of this theory is the Verlinde categories Verp. Understanding the structure of these categories in-depth and how to construct algebraic structures within them are important questions. In this talk, we will start by introducing the Verlinde categories and some of their important properties. We will also give examples of some Lie algebras in symmetric categories in positive characteritic that can be obtained as semisimplification of contragredient Lie algebras in characteristic p. If time allows, we will present some interesting properties that they have. As an application, we will exhibit concrete new examples of Lie algebras in the Verlinde category.
This talk is based on joint work with I. Angiono and G. Sanmarco.
This video was part of the Southeastern Lie Theory Workshop XIV on quantum structure in Lie theory.
