Simple vectorial lie algebras in characteristic 2 and their superizations

Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites, Irina Shchepochkina

Research output: Contribution to journalArticlepeer-review

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 divergencefree 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.

Original languageEnglish (US)
Article number089
Pages (from-to)1-101
Number of pages101
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume16
DOIs
StatePublished - 2020

Keywords

  • Modular vectorial Lie algebra
  • Modular vectorial Lie superalgebra

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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