New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories

Using tensor categories, we present new constructions of several the exceptional simple Lie superalgebras with integer Cartan matrix in characteristic $p = 3$ and 5$ from complete classification modular indecomposable their subquotients over algebraically closed fields by Bouarroudj, Grozman, Leites 2009. Specifically, let $\mathbf{\alpha}_p$ denote kernel Frobenius endomorphism on additive group scheme $\mathbb{G}_a$ an field $p$. The Verlinde category $\mathrm{Ver}_p$ is semisimplification representation $\mathrm{Rep} \ \mathbf{\alpha}_p$, contains super vector spaces as a full subcategory. Each superalgebra construct realized image algebra equipped nilpotent derivation order at most $p$ under functor \mathbf{\alpha}_p$ to $\mathrm{Ver}_p$.