Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations

Abstract

We overview the classifications of simple finite-dimensional modular Lie algebras. In characteristic 2, their list is wider than that in other characteristics; e.g., it contains desuperizations of modular analogs of complex simple vectorial Lie superalgebras. We consider odd parameters of deformations. For all 15 Weisfeiler gradings of the 5 exceptional families, and one Weisfeiler grading for each of 2 serial simple complex Lie superalgebras (with 2 exceptional subseries), we describe their characteristic-2 analogs - new simple Lie algebras. Descriptions of several of these analogs, and of their desuperizations, are far from obvious. One of the exceptional simple vectorial Lie algebras is a previously unknown deform (the result of a deformation) of the characteristic-2 version of the Lie algebra of divergence-free vector fields; this is a new simple Lie algebra with no analogs in characteristics distinct from 2. In characteristic 2, every simple Lie superalgebra can be obtained from a simple Lie algebra by one of the two methods described in arXiv:1407.1695. Most of the simple Lie superalgebras thus obtained from simple Lie algebras we describe here are new.

see pdf-file with index at https://www.emis.de/journals/SIGMA/2020/089/

References in corpus (8)

• Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix
• Classification of supersymmetries
• Towards classification of simple finite dimensional modular Lie superalgebras
• On Gradings Modulo 2 of Simple Lie Algebras in Characteristic 2
• Restricted simple Lie (super)algebras in characteristic $3$
• The normal shapes of the symplectic and contact forms over algebras of divided powers
• Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2
• New simple modular Lie superalgebras as generalized prolongs

Cited by in corpus (10)

• On Gradings Modulo 2 of Simple Lie Algebras in Characteristic 2
• Restricted simple Lie (super)algebras in characteristic $3$
• Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2
• The roots of exceptional modular Lie superalgebras with Cartan matrix
• Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2
• Duflo-Serganova homology for exceptional modular Lie superalgebras with Cartan matrix
• Classification of simple algebras in Deligne category $Rep(S_t)$
• Transitive irreducible Lie superalgebras of vector fields
• Action of vectorial Lie superalgebras on some split supermanifolds
• Representation Theory of General Linear Supergroups in Characteristic 2