New Simple Lie Algebras in Characteristic 2

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)5695-5726
Number of pages32
JournalInternational Mathematics Research Notices
Volume2016
Issue number18
DOIs
StatePublished - Jan 1 2016

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Simple Lie Algebra
Lie Superalgebra
Lie Algebra
Positive Characteristic
Finite Dimensional Algebra
Algebraically closed
Vector Field

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bouarroudj, S., Grozman, P., Lebedev, A., Leites, D., & Shchepochkina, I. (2016). New Simple Lie Algebras in Characteristic 2. 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.

In: International Mathematics Research Notices, Vol. 2016, No. 18, 01.01.2016, p. 5695-5726.

Research output: Contribution to journalArticle

Bouarroudj, S, Grozman, P, Lebedev, A, Leites, D & Shchepochkina, I 2016, 'New Simple Lie Algebras in Characteristic 2', International Mathematics Research Notices, vol. 2016, no. 18, pp. 5695-5726. https://doi.org/10.1093/imrn/rnv327
Bouarroudj, Sofiane ; Grozman, Pavel ; Lebedev, Alexei ; Leites, Dimitry ; Shchepochkina, Irina. / New Simple Lie Algebras in Characteristic 2. In: International Mathematics Research Notices. 2016 ; Vol. 2016, No. 18. pp. 5695-5726.
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