Classification of Simple Lie Superalgebras in Characteristic 2. (30th September 2021) - Bouarroudj, Sofiane; Lebedev, Alexei; Leites, Dimitry; Shchepochkina, Irina
Abstract: All results concern characteristic 2. We describe two procedures; each of which to every simple Lie algebra assigns a simple Lie superalgebra. We prove that every simple finite-dimensional Lie superalgebra is obtained as the result of one of these procedures. For Lie algebras, in addition to the known "classical" restrictedness, we introduce a (2, 4)-structure on the two non-alternating series: orthogonal and Hamiltonian vector fields. For Lie superalgebras, the classical restrictedness of Lie algebras has two analogs: a $2|4$ -structure, which is a direct analog of the classical restrictedness, and a novel $2|2$ -structure—one more analog, a $(2, 4)|4$ -structure on Lie superalgebras is the analog of (2, 4)-structure on Lie algebras known only for non-alternating orthogonal and Hamiltonian series.