Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

In characteristic 2, the classification of modulo 2 gradings of simple Lie algebras is vital for the classification of simple finite dimensional Lie superalgebras: with each grading, a simple Lie superalgebra is associated, (see arXiv:1407.1695 S. Bouarroudj, A. Lebedev, D. Leites, and I. Shchepochkina, "Classifications of simple Lie superalgebras in characteristic 2"). No classification of gradings was known for any type of simple Lie algebras, expect restricted Zassenhaus algebras (a.k.a. Witt algebras, i.e., Lie algebras of vector fields with truncated polynomials as coefficients) on not less than 3 indeterminates. Here we completely describe gradings modulo 2 for several series of simple Lie algebras: special linear, two inequivalent orthogonal, and projectivizations of their derived algebras, except for psl(4) for which a conjecture is given. All of the corresponding superizations are known, but a corollary provesnon-triviality of a deformation of a simple (3|2)-dimensional Liesuperalgebra (new result). For nonrestricted Zassenhaus algebras on one indeterminate of hight n, there is an (n-2)-parametric family of modulo 2 gradings; all but one of the corresponding simple Lie superalgebras are new. Joint work with Alexei Lebedev (Stockholm).