Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Superalgebras

Sofiane Bouarroudj; Antonio J. Calderón; Amir Fernández Ouaridi; Rosa María Navarro

doi:10.1007/s00009-024-02634-z

Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Superalgebras

Sofiane Bouarroudj, Antonio J. Calderón, Amir Fernández Ouaridi, Rosa María Navarro

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the invariants α and β, 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 α and β invariants for some distinguished families of Leibniz superalgebras.

Original language	English (US)
Article number	89
Journal	Mediterranean Journal of Mathematics
Volume	21
Issue number	3
DOIs	https://doi.org/10.1007/s00009-024-02634-z
State	Published - May 2024

Keywords

17A32
17A70
17B30
Abelian ideal
Abelian subalgebra
Leibniz superalgebra
nilpotent
solvable

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-024-02634-z

Cite this

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title = "Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Superalgebras",

abstract = "We study the invariants α and β, 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 α and β invariants for some distinguished families of Leibniz superalgebras.",

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T1 - Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Superalgebras

AU - Bouarroudj, Sofiane

AU - Calderón, Antonio J.

AU - Fernández Ouaridi, Amir

AU - Navarro, Rosa María

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

PY - 2024/5

Y1 - 2024/5

N2 - We study the invariants α and β, 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 α and β invariants for some distinguished families of Leibniz superalgebras.

AB - We study the invariants α and β, 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 α and β invariants for some distinguished families of Leibniz superalgebras.

KW - 17A32

KW - 17A70

KW - 17B30

KW - Abelian ideal

KW - Abelian subalgebra

KW - Leibniz superalgebra

KW - nilpotent

KW - solvable

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JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

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M1 - 89

ER -

Abelian Subalgebras and Ideals of Maximal Dimension in Solvable Leibniz Superalgebras

Abstract

Keywords

ASJC Scopus subject areas

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