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On the classification of simple Lie algebras of dimension seven over fields of characteristic 2

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Abstract

This paper is the second part of paper (Grishkov and Guerreiro in São Paulo J Math Sci v4(1):93–107, 2010) about simple 7-dimensional Lie algebras over an algebraically closed field k of characteristic two. In this paper we prove that all simple 7-dimensional Lie algebras over k of absolute toral rank three are isomorphic to the Cartan algebra \(W_1\) or the Hamilton algebra \(H_2.\) We hope to prove that those algebras are the unique simple 7-dimensional Lie algebras over the field k. Observe that in the case of absolute toral rank 2 this fact was proved in [2].

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References

  1. Grishkov, A., Guerreiro, M.: On simple Lie algebras of dimension seven over a field of characteristic two. São Paulo J. Math. Sci. v.4(1), 93–107 (2010)

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  2. Grishkov, A., Premet, A.: Simple Lie algebras of toral rank two over a field of characteristic two (manuscript)

  3. Skryabin, S.: Toral rank one simple Lie algebras of low characteristics. J. Algebra 200, 650–700 (1998)

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Acknowledgements

Alexander Grishkov acknowledges the financial support from FAPESP, FAPEMIG and CNPq, Brazil and from RFBR, Russia, Grant 16-01-00577a (Sects. 1–3) and from the Russian Science Foundation, Project 16-11-10002 (Sect. 4). Marinês Guerreiro thanks to financial support of FAPESP (Brazil).

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo Rua do Matão 1010, São Paulo, CEP 05508-090, Brazil

    Alexander Grishkov

  2. Omsk State University, n.a. F.M.Dostoevskii pr. Mira 55-A, Omsk, Russia, 644077

    Alexander Grishkov

  3. Departamento de Matemática, Centro de Ciências Exatas e Tecnológicas, Universidade Federal de Viçosa, Viçosa, M.G., Brazil

    Marinês Guerreiro

  4. Universidade Tecnológica Federal do Paraná, R. Cristo Rei, Vila Becker, Toledo, PR, Brazil

    Wilian Francisco de Araujo

Authors
  1. Alexander Grishkov
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  2. Marinês Guerreiro
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  3. Wilian Francisco de Araujo
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Correspondence to Alexander Grishkov.

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Communicated by Vyacheslav Futorny.

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A. Grishkov: Supported by FAPESP and CNPq Processo 307824/2016-0, Brazil and RFBR, Grant 16-01-00577a, Russian. M. Guerreiro: Supported by FAPESP Processo N. 04/07774-2, Brazil.

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Grishkov, A., Guerreiro, M. & de Araujo, W.F. On the classification of simple Lie algebras of dimension seven over fields of characteristic 2. São Paulo J. Math. Sci. 14, 703–713 (2020). https://doi.org/10.1007/s40863-020-00180-6

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  • DOI: https://doi.org/10.1007/s40863-020-00180-6

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