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Nejib Saadaoui

Publications and source records attributed to Nejib Saadaoui.

9 recordsLinked to original sources
arXiv2026

Non-abelian extensions of Hom-Jacobi-Jordan algebras

This paper develops a cohomology theory for Hom-Jacobi-Jordan algebras using and applies it to classify non-abelian extensions. The main result establishes that equivalence classes of split extensions of a Hom-Jacobi-Jordan algebra $J$ by $V$ are in bijection with the second cohomology group $H^2(J,V)$, generalizing classical results from Lie and Leibniz algebra theory. We characterize extensions explicitly through 2-cocycles $(\rho, \theta)$ satisfying compatibility conditions, and provide complete classifications of low-dimensional cases.

math.RA↗
arXiv2024

Extensions of (metric) Hom-Jacobi-Jordan algebras

The main purpose of this paper is to provide a second cohomology group of a (metric) Hom-Jacobi algebra with coefficients in a given representation. Moreover, we show that second cohomology group classifies abelian extensions of a (metric) Hom-Jacobi algebra algebra by a representation.

math.RA↗
arXiv2021

Split extensions of BiHom-Lie algebras

In this paper, we introduce the notion of split extension of BiHom- Lie algebra and construct the corresponding cohomology. Also, we establish a one-to-one correspondence between the equivalence classes of extensions of a BiHom-Lie algebra L by an abelian BiHom-Lie algebra V and its second cohomology group.

math.RA↗
arXiv2021

On $(λ,μ,γ)$-derivations of BiHom-Lie algebras

In this paper, we generalize the results about generalized derivations of Lie algebras to the case of BiHom-Lie algebras. In particular we give the classification of generalized derivations of Heisenberg BiHom-Lie algebras. The definition of the generalized derivation depends on some parameters $ (λ,μ,γ)\in \mathbb{C}^{3}. $ In particular for $(λ,μ,γ)=(1,1,1)$, we obtain classical concept of derivation of BiHom-Lie algebra and for $(λ,μ,γ)=(1,1,0) $ we obtain the centroid of BiHom-Lie algebra. We give classifications of $ 2 $-dimensional BiHom-Lie algebra, centroides and derivations of $ 2 $-dimensional BiHom-Lie algebras.

math.RA↗
arXiv2021

Classification, centroids and derivations of two-dimensional Hom-Leibniz algebras

Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids and derivations of multiplicative Hom-Leibniz algebras are considered including the detailed study of 2-dimensional Hom-Leibniz algebras.

math.RA↗
arXiv2020

Non-abelian cohomology and extensions of Hom-algebras via the $\boldsymbol{\beta}$-Nijenhuis--Richardson bracket

This paper develops a cohomology theory for Hom-Leibniz algebras using the $\beta$-Nijenhuis--Richardson bracket and applies it to classify non-abelian extensions. We introduce left, and right versions of the bracket, each defining a graded Lie algebra structure on the space of $\beta$-cochains. The main result establishes that equivalence classes of split extensions of a Hom-Leibniz algebra $L$ by $V$ are in bijection with the second cohomology space $H^2(L,V)$, generalizing classical results from Lie and Leibniz algebra theory. We characterize extensions explicitly through 2-cocycles $(\lambda_l, \lambda_r, \theta)$ and provide complete classifications of low-dimensional cases.

math.RA↗
arXiv2013

Second Cohomology of q-deformed Witt superalgebras

The purpose of this paper is to compute the second adjoint cohomology group of q-deformed Witt superalgebras. They are Hom-Lie superalgebras obtained by q-deformation of Witt Lie superalgebra, that is one considers $σ$-derivations instead of classical derivations.

math.RA↗