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Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Superalgebras

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Abstract

We study the invariants \(\alpha \) and \(\beta \), which correspond to the dimension of an abelian subalgebra (ideal resp.) of maximal dimension, in the context of Leibniz superalgebras. We prove that these invariants coincide if there is an abelian subalgebra of codimension one. We also examine the case in which the abelian subalgebras of maximal dimension are of codimension two. Finally, we study the \(\alpha \) and \(\beta \) invariants for some distinguished families of Leibniz superalgebras.

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Authors and Affiliations

  1. Division of Science and Mathematics, New York University Abu Dhabi, PO Box 129188, Abu Dhabi, United Arab Emirates

    Sofiane Bouarroudj

  2. Dpto. de Matemáticas, Universidad de Cádiz, Puerto Real, Spain

    Antonio J. Calderón & Amir Fernández Ouaridi

  3. Centre for Mathematics, Universidade de Coimbra, Coimbra, Portugal

    Amir Fernández Ouaridi

  4. Dpto. de Matemáticas, Universidad de Extremadura, Cáceres, Spain

    Rosa María Navarro

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  1. Sofiane Bouarroudj
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  2. Antonio J. Calderón
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  3. Amir Fernández Ouaridi
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  4. Rosa María Navarro
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All authors have contributed equally to this work.

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Correspondence to Amir Fernández Ouaridi.

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This work was supported by Ministerio de Economía y Competitividad (Spain), under Grant No. PID2020-115155GB-I00 (European FEDER support included, EU) and by Junta de Andalucía, Consejería de Universidad, Investigación e Innovación: ProyExcel_00780 “Operator theory: An interdisciplinary approach”. The third author was supported by the Spanish Government through the Ministry of Universities grant ‘Margarita Salas’, funded by the European Union—NextGenerationEU and by the Centre for Mathematics of the University of Coimbra—UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES.

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Bouarroudj, S., Calderón, A.J., Fernández Ouaridi, A. et al. Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Superalgebras. Mediterr. J. Math. 21, 89 (2024). https://doi.org/10.1007/s00009-024-02634-z

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  • DOI: https://doi.org/10.1007/s00009-024-02634-z

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