The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e19" altimg="si31.gif"><mml:mi>c</mml:mi></mml:math>-nilpotent Schur <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e24" altimg="si32.gif"><mml:mi mathvariant="sans-serif">Lie</mml:mi></mml:math>-multiplier of Leibniz algebras

Biyogmam, Guy Roger; Casas, J. M.

doi:10.1016/j.geomphys.2018.12.021

Cited by 13 publications

(3 citation statements)

References 27 publications

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“…These notions of Lie-center and Lie-centralizer were studied in [4,6,8,9] as a result of approaching the relative theory of Leibniz algebras with respect to the Liezation functor. Note that Z Lie (g…”

Section: Leibniz Algebrasmentioning

confidence: 99%

Leibniz algebras with absolute maximal Lie subalgebras

Biyogmam

Tcheka

2020

ADM

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A Lie subalgebra of a given Leibniz algebra is said to be an absolute maximal Lie subalgebra if it has codimension one. In this paper, we study some properties of non-Lie Leibniz algebras containing absolute maximal Lie subalgebras. When the dimension and codimension of their Lie-center are greater than two, we refer to these Leibniz algebras as s-Leibniz algebras (strong Leibniz algebras). We provide a classification of nilpotent Leibniz s-algebras of dimension up to five.

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Section: Leibniz Algebrasmentioning

confidence: 99%

Leibniz algebras with absolute maximal Lie subalgebras

Biyogmam

Tcheka

2020

ADM

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“…The category of Lie algebras forms a Birkhoff subcategory of the category of Leibniz algebras. This means that we can study relative commutator theory o Leibniz algebras respect to Lie, giving rise to interesting developments in the comprehension of both algebraic structures [2,3,5,7,33]. Moreover, the interplay between these two categories can be somehow tricky, since it is also possible to find Leibniz algebras as a subcategory of a certain type of Lie algebras [25], although many interesting categorical properties are not preserved [15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

On some properties of $\mathsf{Lie}$-centroids of Leibniz algebras

Casas,

García-Martínez,

Pachego-Rego

2021

Preprint

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“…The approached properties are closely related to the relative notions of central extension in a semi-abelian category with respect to a Birkhoff subcategory [11,14]. A recent research line deals with the development of absolute properties of Leibniz algebras (absolute are the usual properties and it means relative to the abelianization functor) in the relative setting (with respect to the Liezation functor); in general, absolute properties have the corresponding relative ones, but not all absolute properties immediately hold in the relative case, so new requirements are needed as it can be seen in the following papers [3,4,5,8,10,19].…”

Section: Introductionmentioning

confidence: 99%

Lie-central derivations, Lie-centroids and Lie-stem Leibniz algebras

Biyogmam

Casas

Rego³

2019

Preprint

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In this paper, we introduce the notion Lie-derivation. This concept generalizes derivations for non-Lie Leibniz algebras. We study these Liederivations in the case where their image is contained in the Lie-center, call them Lie-central derivations. We provide a characterization of Lie-stem Leibniz algebras by their Lie-central derivations, and prove several properties of the Lie algebra of Lie-central derivations for Lie-nilpotent Leibniz algebras of class 2. We also introduce ID * -Lie-derivations. A ID * -Lie-derivation of a Leibniz algebra g is a Lie-derivation of g in which the image is contained in the second term of the lower Lie-central series of g, and that vanishes on Lie-central elements. We provide an upperbound for the dimension of the Lie algebra ID Lie * (g) of ID * -Lie-derivation of g, and prove that the sets ID Lie * (g) and ID Lie * (q) are isomorphic for any two Lie-isoclinic Leibniz algebras g and q.

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The c-nilpotent Schur Lie-multiplier of Leibniz algebras

Cited by 13 publications

References 27 publications

Leibniz algebras with absolute maximal Lie subalgebras

Leibniz algebras with absolute maximal Lie subalgebras

On some properties of $\mathsf{Lie}$-centroids of Leibniz algebras

Lie-central derivations, Lie-centroids and Lie-stem Leibniz algebras

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