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Classification, Centroids and Derivations of Two-Dimensional Hom-Leibniz 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

Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids and derivations of multiplicative Hom-Leibniz algebras are considered including the detailed study of 2-dimensional Hom-Leibniz 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. Department of Mathematics, College of Sciences and Arts in Gurayat, Jouf University, Sakakah, Saudi Arabia

    Anja Arfa

  2. Faculty of Sciences, University of Sfax, BP 1171, 3000, Sfax, Tunisia

    Anja Arfa

  3. Institut Supérieur d’Informatique et de Multimédia de Gabès, Université de Gabès, Campus universitaire-BP 122, 6033 Cité El Amel 4, Gabès, Tunisie

    Nejib Saadaoui

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

    Sergei Silvestrov

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  1. Anja Arfa
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Correspondence to Nejib Saadaoui .

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  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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Arfa, A., Saadaoui, N., Silvestrov, S. (2023). Classification, Centroids and Derivations of Two-Dimensional Hom-Leibniz 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_3

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