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Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Algebras

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Abstract

In this paper, we compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional Leibniz algebras. We study Leibniz algebras containing abelian subalgebras of codimension 1, solvable and supersolvable Leibniz algebras for codimensions 1 and 2, nilpotent Leibniz algebras in case of codimension 2, and we also analyze the case of k-abelian p-filiform Leibniz algebras. Throughout the paper, we also give examples to clarify some results and the need for restrictions on the underlying field.

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Acknowledgements

The paper was partially supported by US-1262169, P20_01056, MTM2016-75024-P and FEDER.

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Authors and Affiliations

  1. Dpto. de Ingeniería, Universidad Loyola Andalucía, Av. de las Universidades, s/n, 41704, Dos Hermanas, Sevilla, Spain

    Manuel Ceballos

  2. Department of Mathematics, Lancaster University, Lancaster, LA1 4YF, United Kingdom

    David A. Towers

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  1. Manuel Ceballos
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  2. David A. Towers
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Correspondence to Manuel Ceballos.

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Ceballos, M., Towers, D.A. Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Algebras. Mediterr. J. Math. 20, 97 (2023). https://doi.org/10.1007/s00009-023-02306-4

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  • DOI: https://doi.org/10.1007/s00009-023-02306-4

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