I will present new constructions of several of the exceptional simple Lie superalgebras with integer Cartan matrix in characteristic p = 3 and p = 5, which were classified in [1]. These include the Elduque and Cunha Lie superalgebras. Specifically, let ap denote the kernel of the Frobenius endomorphism on the additive group scheme Ga over an algebraically closed field of characteristic p. The Verlinde category Verp is the semisimplification of the representation category Rep ap, and Verp contains the category of super vector spaces as a full subcategory. Each exceptional Lie superalgebra we construct is realized as the image of an exceptional Lie algebra equipped with a nilpotent derivation of order at most p under the semisimplification functor from Rep ap to Verp. The content of this talk can primarily be found in [2] and [3].
Keywords: modular Lie superalgebras, symmetric tensor categories Mathematics Subject Classification 2020: 17B, 18M20
References:
[1] S. Bouarroudj, P. Grozman, and D. Leites, Classification of simple finite- dimensional modular Lie superalgebras with Cartan matrix, Symmetry, Inte- grability and Geometry: Methods and Applications (SIGMA) v. 5 (2009), no. 060, 63 pages.
[2] A.S. Kannan, New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories, Trans- formation Groups (2022).
[3] P. Etingof, and A.S. Kannan, Lectures On Symmetric Tensor Categories, arXiv:2103.04878 (2021).
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