## 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 language | English (US) |
---|---|

Article number | 089 |

Pages (from-to) | 1-101 |

Number of pages | 101 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 16 |

DOIs | |

State | Published - 2020 |

## Keywords

- Modular vectorial Lie algebra
- Modular vectorial Lie superalgebra

## ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Geometry and Topology