arXiv subjects

Bouzid Mosbahi

Publications and source records attributed to Bouzid Mosbahi.

25 records · Page 2Linked to original sources

arXiv2023

Cohomology and deformation theory of $\mathcal{O}$-operators on Hom-Lie conformal algebras

In the present paper, we aim to introduce the cohomology of $\mathcal{O}$-operators defined on the Hom-Lie conformal algebra concerning the given representation. To obtain the desired results, we describe three different cochain complexes and discuss the interrelation of their coboundary operators. And show that differential maps on the graded Lie algebra can also be defined by using the Maurer-Cartan element. We further find out that, the $\mathcal{O}$-operator on the given Hom-Lie conformal algebra serves as a Maurer-Cartan element and it leads to acquiring the notion of a differential map in terms of $\mathcal{O}$-operator $δ_{\mathcal{T}}$. Next, we provide the notion of Hom-pre-Lie conformal algebra, that induces a sub-adjacent Hom-Lie conformal algebra structure. The differential $δ_{β,α}$ of this sub-adjacent Hom-Lie conformal algebra is related to the differential $δ_{\mathcal{T}}$. Finally, we provide the deformation theory of $\mathcal{O}$-operators on the Hom-Lie conformal algebras as an application to the cohomology theory, where we discuss linear and formal deformations in detail.

math.RA↗

arXiv2023

Quasi-Centroids and Quasi-Derivations of Low Dimensional Associative Algebras

In this paper, we present some basic properties concerning the quasi-derivation algebra $QDer(\mathcal{A})$ and the quasi-centroid algebra $QC(\mathcal{A})$ of associative algebra $\mathcal{A}$. Furthermore, using the result on classification of two, three and four dimensional associative algebra, we compute, for all two, three and four dimensional associative algebras, quasi-derivation algebra $QDer(\mathcal{A})$ and the quasi-centroid algebra $QC(\mathcal{A})$ algebras and give their corresponding dimension.

math.RA↗

arXiv2023

Classification of tridendriform algebra and related structures

The classification of algebraic structures and their derivations is an important and ongoing research area in mathematics and physics, and various results have been obtained in this field. This article presents the classification of tridendriform algebras that was first studied by Loday and Ronco, including an analysis of structure constant equations using computer algebra software. We further explicitly classify the derivations and centroids of tridendriform algebras, showing that there are only trivial derivations for $2$- and $3$-dimensional algebras but $21$ non-isomorphic derivations for $4$-dimensional tridendriform algebras with dimension range from $1$ to $5$. Additionally, for centroids (centroid and quasi-centroid), there are trivial isomorphism classes for $2$ dimensional tridendriform algebra, $6$ non-isomorphic classes for $3$-dimensional tridendriform algebras and $21$ for $4$-dimensional algebras. The dimensions range for centroid is from $1$ to $5$, whereas it is from $1$ to $10$ for quasi-centroid.

math.RA↗

arXiv2023

Classification, $α$-Inner Derivations and $α$-Centroids of Finite-Dimensional Complex Hom-Trialgebras

In the current research work, our basic objective is to investigate the stucture of Hom-associative trialgebras. Next, we build up one important class of Hom-associative trialgebras and provide properties of right, left and meddle operations in Hom-associative trialgebras. Furthermore, we describe the classification of $n$-dimensional Hom-associative trialgebras for $n\leq 3$. Additionally, the properties of the Inner-derivations and centroids are identified and discussed. Eventually the Inner-derivations and centroids are computed.

math.RA↗

arXiv2023

Classification, Derivations and Centroids of Low-Dimensional Complex BiHom-Trialgebras

The basic objective of this research work is to investigate the stucture of BiHom-associative trialgebras.\,In this respect we build up one important class of BiHom-trialgebras and determine properties of right, left and middle operations in BiHom-associative trialgebras.\,We provide a classification of $n$-dimensional BiHom-trialgebras for $n\leq3$.\,Relying upon the classification result of BiHom-associative trialgebras, the derivations and centroids of low-dimensional BiHom-associative trialgebras are characterized.\,Certain properties of the centroids in light of BiHom-associative trialgebras are reviwed the centroids of low-dimensional BiHom-associative trialgebras are computed.

math.RA↗

arXiv2023

Classification, Derivations and Centroids of Low-Dimensional Real Trialgebras

In this paper we study the structure and the algebraic varieties of associative trialgebras. We provide a classification of n-dimensional associative trialgebras for n $\leq$ 4. Using the classification result of associative trialgebras, we describe the derivations and centroids of low-dimensional associative trialgebras. We review some proprieties of the centroids in light of associative trialgebras and and we calculate the centroids of low-dimensional associative trialgebras.

math.RA↗

arXiv2023

Cohomology of compatible BiHom-Lie algebras

This paper defines compatible BiHom-Lie algebras by twisting the compatible Lie algebras by two linear commuting maps. We show the characterization of compatible BiHom-Lie algebra as a Maurer-Cartan element in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible BiHom-Lie algebras.

math.RA↗