Towards classification of simple finite dimensional modular Lie superalgebras

Abstract

A way to construct (conjecturally all) simple finite dimensional modular Lie (super)algebras over algebraically closed fields of characteristic not 2 is offered. In characteristic 2, the method is supposed to give only simple Lie (super)algebras graded by integers and only some of the non-graded ones). The conjecture is backed up with the latest results computationally most difficult of which are obtained with the help of Grozman's software package SuperLie.

arXiv comment10 pages

References in corpus (6)

• Invariant operators on supermanifolds and Standard Models
• Classification of supersymmetries
• Some new simple modular Lie superalgebras
• Non-degenerate bilinear forms in characteristic 2, related contact forms, simple Lie algebras and superalgebras
• The five exceptional simple Lie superalgebras of vector fields
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Cited by in corpus (6)

• Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations
• Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras
• Simple prolongs of the non-positive parts of graded Lie algebras with Cartan matrix in characteristic 2
• Deformations of Symmetric Simple Modular Lie (Super)Algebras
• Lie algebra deformations in characteristic 2
• Classification of simple algebras in Deligne category $Rep(S_t)$