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On \((\lambda ,\mu ,\gamma )\)-Derivations of BiHom-Lie Algebras

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Non-commutative and Non-associative Algebra and Analysis Structures (SPAS 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 426))

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Abstract

In this paper, we generalize the results about generalized derivations of Lie algebras to the case of BiHom-Lie algebras. In particular we give the classification of generalized derivations of Heisenberg BiHom-Lie algebras. The definition of the generalized derivation depends on some parameters \( (\lambda ,\mu ,\gamma )\in \mathbb {C}^{3}\). In particular for \((\lambda ,\mu ,\gamma )=(1,1,1)\), we obtain classical concept of derivation of BiHom-Lie algebra and for \((\lambda ,\mu ,\gamma )=(1,1,0) \) we obtain the centroid of BiHom-Lie algebra. We give classifications of 2-dimensional BiHom-Lie algebra, centroids and derivations of 2-dimensional BiHom-Lie algebras.

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Acknowledgements

Sergei Silvestrov is grateful to the Royal Swedish Academy of Sciences for partial support.

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Authors and Affiliations

  1. Université de Gabès, Institut Supérieur de l’Informatique Medenine, Rue Djerba km3, B.P 283, Medenine, 4100, Tunisie

    Nejib Saadaoui

  2. Division of Mathematics and Physics, School of Education, Culture and Communication, Mälardalen University, Box 883, 72123, Västerås, Sweden

    Sergei Silvestrov

Authors
  1. Nejib Saadaoui
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  2. Sergei Silvestrov
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Correspondence to Nejib Saadaoui .

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Editors and Affiliations

  1. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

  2. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden

    Anatoliy Malyarenko

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Saadaoui, N., Silvestrov, S. (2023). On \((\lambda ,\mu ,\gamma )\)-Derivations of BiHom-Lie Algebras. In: Silvestrov, S., Malyarenko, A. (eds) Non-commutative and Non-associative Algebra and Analysis Structures. SPAS 2019. Springer Proceedings in Mathematics & Statistics, vol 426. Springer, Cham. https://doi.org/10.1007/978-3-031-32009-5_28

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