### Abstract

Several improvements of the Kostrikin-Shafarevich method conjecturally producing all simple finite-dimensional Lie algebras over algebraically closed fields of any positive characteristic were recently suggested; the list of examples obtained by the improved method becomes richer but in characteristic 2 it is far from being saturated. We investigate one of the steps of our version of the method; in characteristic 2 we describe several new simple Lie algebras and interpret several other simple Lie algebras, previously known only as sums of their components, as Lie algebras of vector fields. Several new simple Lie superalgebras can be constructed from the newly found simple Lie algebras. We also describe one new simple Lie superalgebra in characteristic 3; it is the only simple Lie superalgebra missed in the approach taken in [6].

Original language | English (US) |
---|---|

Pages (from-to) | 5695-5726 |

Number of pages | 32 |

Journal | International Mathematics Research Notices |

Volume | 2016 |

Issue number | 18 |

DOIs | |

State | Published - Jan 1 2016 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*International Mathematics Research Notices*,

*2016*(18), 5695-5726. https://doi.org/10.1093/imrn/rnv327

**New Simple Lie Algebras in Characteristic 2.** / Bouarroudj, Sofiane; Grozman, Pavel; Lebedev, Alexei; Leites, Dimitry; Shchepochkina, Irina.

Research output: Contribution to journal › Article

*International Mathematics Research Notices*, vol. 2016, no. 18, pp. 5695-5726. https://doi.org/10.1093/imrn/rnv327

}

TY - JOUR

T1 - New Simple Lie Algebras in Characteristic 2

AU - Bouarroudj, Sofiane

AU - Grozman, Pavel

AU - Lebedev, Alexei

AU - Leites, Dimitry

AU - Shchepochkina, Irina

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Several improvements of the Kostrikin-Shafarevich method conjecturally producing all simple finite-dimensional Lie algebras over algebraically closed fields of any positive characteristic were recently suggested; the list of examples obtained by the improved method becomes richer but in characteristic 2 it is far from being saturated. We investigate one of the steps of our version of the method; in characteristic 2 we describe several new simple Lie algebras and interpret several other simple Lie algebras, previously known only as sums of their components, as Lie algebras of vector fields. Several new simple Lie superalgebras can be constructed from the newly found simple Lie algebras. We also describe one new simple Lie superalgebra in characteristic 3; it is the only simple Lie superalgebra missed in the approach taken in [6].

AB - Several improvements of the Kostrikin-Shafarevich method conjecturally producing all simple finite-dimensional Lie algebras over algebraically closed fields of any positive characteristic were recently suggested; the list of examples obtained by the improved method becomes richer but in characteristic 2 it is far from being saturated. We investigate one of the steps of our version of the method; in characteristic 2 we describe several new simple Lie algebras and interpret several other simple Lie algebras, previously known only as sums of their components, as Lie algebras of vector fields. Several new simple Lie superalgebras can be constructed from the newly found simple Lie algebras. We also describe one new simple Lie superalgebra in characteristic 3; it is the only simple Lie superalgebra missed in the approach taken in [6].

UR - http://www.scopus.com/inward/record.url?scp=84994410025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994410025&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnv327

DO - 10.1093/imrn/rnv327

M3 - Article

VL - 2016

SP - 5695

EP - 5726

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 18

ER -