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On Ideals and Derived and Central Descending Series of n-ary Hom-Algebras

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Non-Associative Algebras and Related Topics (NAART 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 427))

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Abstract

The aim of this work is to explore some properties of n-ary skew-symmetric Hom-algebras and n-Hom-Lie algebras related to their ideals, derived series and central descending series. We extend the notions of derived series and central descending series to n-ary skew-symmetric Hom-algebras and provide various general conditions for their members to be Hom-subalgebras, weak ideals or Hom-ideals in the algebra or relatively to each other. In particular we study the invariance under the twisting maps of the derived series and central descending series and their subalgebra and ideal properties for a class of 3-dimensional Hom-Lie algebras and some 4-dimensional 3-Hom-Lie algebras. We also introduce a type of generalized ideals in n-ary Hom-algebras and present a few basic properties.

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Acknowledgements

Elvice Ongong’a and Stephen Mboya are grateful to the International Science Program (ISP), Uppsala University for the support in the framework of the Eastern Africa Universities Mathematics Programme (EAUMP). Elvice Ongong’a, Stephen Mboya and Abdennour Kitouni also thank the research environment in Mathematics and Applied Mathematics (MAM), the Division of Mathematics and Physics of the School of Education, Culture and Communication at Mälardalen University for hospitality and creating excellent conditions for research and research education. The authors are grateful to anonymous referees for helpful suggestions.

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Authors and Affiliations

  1. Division of Mathematics and Physics, Mälardalen University, Box 833, 72123, Västerås, Sweden

    Abdennour Kitouni & Sergei Silvestrov

  2. Department of Mathematics, University of Nairobi, Box 30197, Nairobi, Kenya

    Stephen Mboya & Elvice Ongong’a

  3. Division of Mathematics and Physics, Mälardalen University, Box 833, 72123, Västerås, Sweden

    Stephen Mboya

  4. Strathmore Institute of Mathematical Sciences, Strathmore University, Box 59857, Nairobi, Kenya

    Elvice Ongong’a

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  1. Abdennour Kitouni
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  2. Stephen Mboya
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  3. Elvice Ongong’a
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  4. Sergei Silvestrov
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Correspondence to Sergei Silvestrov .

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Editors and Affiliations

  1. Mathematics, University of Coimbra, Coimbra, Portugal

    Helena Albuquerque

  2. Department of Mathematics, Centre for Mathematics of the University of Coimbra, Coimbra, Portugal

    Jose Brox

  3. Mathematics, University of Oviedo, Oviedo, Spain

    Consuelo Martínez

  4. CMUC-Centre for Mathematics of the University of Coimbra, CeBER-Centre for Business and Economics Research, Faculty of Economics, University of Coimbra, Coimbra, Portugal

    Paulo Saraiva

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Kitouni, A., Mboya, S., Ongong’a, E., Silvestrov, S. (2023). On Ideals and Derived and Central Descending Series of n-ary Hom-Algebras. In: Albuquerque, H., Brox, J., Martínez, C., Saraiva, P. (eds) Non-Associative Algebras and Related Topics. NAART 2020. Springer Proceedings in Mathematics & Statistics, vol 427. Springer, Cham. https://doi.org/10.1007/978-3-031-32707-0_17

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