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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 089, 101 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.089
(Mi sigma1626)
 

This article is cited in 2 scientific papers (total in 2 papers)

Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations

Sofiane Bouarroudja, Pavel Grozmanb, Alexei Lebedevb, Dimitry Leitesac, Irina Shchepochkinad

a New York University Abu Dhabi, Division of Science and Mathematics, P.O. Box 129188, United Arab Emirates
b Equa Simulation AB, Råsundavägen 100, Solna, Sweden
c Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden
d Independent University of Moscow, Bolshoj Vlasievsky per. 11, 119002 Moscow, Russia
References:
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.
Keywords: modular vectorial Lie algebra, modular vectorial Lie superalgebra.
Funding agency Grant number
New York University Abu Dhabi AD 065 NYUAD
S.B. and D.L. were partly supported by the grant AD 065 NYUAD.
Received: September 25, 2019; in final form August 25, 2020; Published online September 24, 2020
Bibliographic databases:
Document Type: Article
MSC: 17B50, 17B20, 70F25
Language: English
Citation: Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites, Irina Shchepochkina, “Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations”, SIGMA, 16 (2020), 089, 101 pp.
Citation in format AMSBIB
\Bibitem{BouGroLeb20}
\by Sofiane~Bouarroudj, Pavel~Grozman, Alexei~Lebedev, Dimitry~Leites, Irina~Shchepochkina
\paper Simple Vectorial Lie Algebras in Characteristic~2 and their Superizations
\jour SIGMA
\yr 2020
\vol 16
\papernumber 089
\totalpages 101
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\crossref{https://doi.org/10.3842/SIGMA.2020.089}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85091525834}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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