Classification of Simple Lie Superalgebras in Characteristic 2

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.