S. Bouarroudj, P. Ya. Grozman, D. A. Leites, “New Simple Modular Lie Superalgebras as Generalized Prolongs”, Funktsional. Anal. i Prilozhen., 42:3 (2008), 1–9; Funct. Anal. Appl., 42:3 (2008), 161

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Funktsional'nyi Analiz i ego Prilozheniya, 2008, Volume 42, Issue 3, Pages 1–9
DOI: https://doi.org/10.4213/faa2924 (Mi faa2924)

This article is cited in 12 scientific papers (total in 12 papers)

New Simple Modular Lie Superalgebras as Generalized Prolongs

S. Bouarroudj^a, P. Ya. Grozman^b, D. A. Leites^b

^a United Arab Emirates University
^b Stockholm University

Full-text PDF (236 kB) Citations (12)

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DOI: https://doi.org/10.4213/faa2924

Abstract: Over algebraically closed fields of characteristic

$p>2$ , — prolongations of simple finite dimensional Lie algebras and Lie superalgebras with Cartan matrix are studied for certain simplest gradings of these algebras. We discover several new simple Lie superalgebras, serial and exceptional, including super versions of Brown and Melikyan algebras, and thus corroborate the super analog of the Kostrikin–Shafarevich conjecture. Simple Lie superalgebras with

$2\times 2$ Cartan matrices are classified.

Keywords: Cartan prolong, Lie superalgebra.

Received: 09.12.2006

English version:
Functional Analysis and Its Applications, 2008, Volume 42, Issue 3, Pages 161–168
DOI: https://doi.org/10.1007/s10688-008-0025-3

Bibliographic databases:

Document Type: Article

UDC: 512.554.38

Language: Russian

Citation: S. Bouarroudj, P. Ya. Grozman, D. A. Leites, “New Simple Modular Lie Superalgebras as Generalized Prolongs”, Funktsional. Anal. i Prilozhen., 42:3 (2008), 1–9; Funct. Anal. Appl., 42:3 (2008), 161–168

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Linking options:

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https://doi.org/10.4213/faa2924

https://www.mathnet.ru/eng/faa/v42/i3/p1

This publication is cited in the following 12 articles:

Sofiane Bouarroudj, Pavel Grozman, Dimitry Leites, “Deformations of Symmetric Simple Modular Lie (Super)Algebras”, SIGMA, 19 (2023), 031, 66 pp.
Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites, “Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov)”, SIGMA, 19 (2023), 032, 73 pp.
Sofiane Bouarroudj, Alexei Lebedev, Dimitry Leites, Irina Shchepochkina, “Classification of Simple Lie Superalgebras in Characteristic 2”, International Mathematics Research Notices, 2023:1 (2023), 54
Arun S. Kannan, “New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories”, Transformation Groups, 2022
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.
Saïd Benayadi, Sofiane Bouarroudj, Mounir Hajli, “Double Extensions of Restricted Lie (Super)Algebras”, Arnold Math J., 6:2 (2020), 231
S. Bouarroudj, A. O. Krutov, A. V. Lebedev, D. A. Leites, I. M. Shchepochkina, “Restricted Lie (Super)Algebras in Characteristic 3”, Funct. Anal. Appl., 52:1 (2018), 49–52
Bouarroudj S., Krutov A., Leites D., Shchepochkina I., “Non-Degenerate Invariant (Super)Symmetric Bilinear Forms on Simple Lie (Super)Algebras”, Algebr. Represent. Theory, 21:5 (2018), 897–941
Bouarroudj S., Lebedev A., Leites D., Shchepochkina I., “Lie Algebra Deformations in Characteristic 2”, Math. Res. Lett., 22:2 (2015), 353–402
Zhu Wei, Qingcheng Zhang, Yongzheng Zhang, Chunyue Wang, “Simple Modules for Modular Lie SuperalgebrasW(0∣n),S(0∣n), andK(n)”, Advances in Mathematical Physics, 2015 (2015), 1
Bouarroudj S., Grozman P., Lebedev A., Leites D., “Divided power (co)homology. Presentations of simple finite dimensional modular Lie superalgebras with Cartan matrix”, Homology Homotopy Appl., 12:1 (2010), 237–278
Sofiane Bouarroudj, Pavel Grozman, Dimitry Leites, “Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix”, SIGMA, 5 (2009), 060, 63 pp.

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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