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On n-ary Generalization of BiHom-Lie Algebras and BiHom-Associative Algebras

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Algebraic Structures and Applications (SPAS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 317))

Abstract

The aim of this paper is to introduce n-ary BiHom-algebras, generalizing BiHom-algebras. We introduce an alternative concept of BiHom-Lie algebra called BiHom-Lie-Leibniz algebra and study various type of n-ary BiHom-Lie algebras and BiHom-associative algebras. We show that n-ary BiHom-Lie-Leibniz algebra can be represented by BiHom-Lie-Leibniz algebra through fundamental objects. Moreover, we provide some key constructions and study n-ary BiHom-Lie algebras induced by \((n-1)\)-ary BiHom-Lie algebra.

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Acknowledgements

A. Kitouni is grateful to the research environment in Mathematics and Applied Mathematics (MAM), Division of Applied Mathematics at the School of Education, Culture and Communication at Mälardalen University, Västerås, Sweden for providing support and excellent research environment during his visits to Mälardalen University when part of the work on this paper has been performed.

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Authors and Affiliations

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

    Abdennour Kitouni & Sergei Silvestrov

  2. Université de Haute-Alsace, 4 rue des Frères Lumière, 68093, Mulhouse, France

    Abdenacer Makhlouf

Authors
  1. Abdennour Kitouni
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  2. Sergei Silvestrov
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  3. Abdenacer Makhlouf
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Correspondence to Abdennour Kitouni .

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Editors and Affiliations

  1. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

  2. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Anatoliy Malyarenko

  3. Division of Applied Mathematics, School of Education, Culture and Communication, Mälardalen University, Västerås, Sweden

    Milica Rančić

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Kitouni, A., Silvestrov, S., Makhlouf, A. (2020). On n-ary Generalization of BiHom-Lie Algebras and BiHom-Associative Algebras. In: Silvestrov, S., Malyarenko, A., Rančić, M. (eds) Algebraic Structures and Applications. SPAS 2017. Springer Proceedings in Mathematics & Statistics, vol 317. Springer, Cham. https://doi.org/10.1007/978-3-030-41850-2_5

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