On Gradings Modulo 2 of Simple Lie Algebras in Characteristic 2
Andrey Krutov, Alexei Lebedev

TL;DR
This paper classifies modulo 2 gradings of simple Lie algebras in characteristic 2, revealing new superalgebras and a non-trivial deformation, which aids in understanding Lie superalgebra structures.
Contribution
It provides the first complete classification of modulo 2 gradings for several series of simple Lie algebras in characteristic 2, including new superalgebras and deformation results.
Findings
Complete classification of gradings for special linear and orthogonal series.
Identification of a parametric family of gradings for Zassenhaus algebras.
Discovery of a non-trivial deformation of a 3|2-dimensional Lie superalgebra.
Abstract
The ground field in the text is of 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. No classification of gradings was known for any type of simple Lie algebras, bar restricted Jacobson-Witt algebras (i.e., the first derived of the 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 Lie algebras and their simple relatives: of special linear series, its projectivizations, and projectivizations of the derived Lie algebras of two inequivalent orthogonal series (except for ). The classification of gradings is new, but all of the corresponding superizations…
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