arXiv subjects
Publications and source records attributed to Faouzi Ammar.
The purpose of this paper is define the representation and the cohomology of n-ary-Nambu-Lie superalgebras. Morever we study extensions and provide the computation of the derivations and second cohomology group of super w_1 3-algebra
The purpose of this paper is to study global deformations of Hom-Leibniz algebras. We introduce a cohomology for Hom-Leibniz algebras with values in a Hom-module, characterize versal deformations and provide examples.
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.
The purpose of this paper is to define the representation and the cohomology of Hom-Lie superalgebras. Moreover we study Central extensions and provide as application the computations of the derivations and second cohomology group of q-deformed Witt superalgebra.
The purpose of this paper is to introduce and study quadratic $n$-ary Hom-Nambu algebras, which are $n$-ary Hom-Nambu algebras with an invariant, nondegenerate and symmetric bilinear forms that are also $α$-symmetric and $β$-invariant where $α$ and $β$ are twisting maps. We provide constructions of these $n$-ary algebras by using twisting principles, tensor product and T*-extension. Also is discussed their connections with representation theory and centroids. Moreover we show that one may derive from quadratic $n$-ary Hom-Nambu algebra ones of increasingly higher arities and that under suitable assumptions it reduces to a quadratic $(n-1)$-ary Hom-Nambu algebra.
The purpose of this paper is to define cohomology structures on Hom-associative algebras and Hom-Lie algebras. The first and second coboundary maps were introduced by Makhlouf and Silvestrov in the study of one-parameter formal deformations theory. Among the relevant formulas for a generalization of Hochschild cohomology for Hom-associative algebras and a Chevalley-Eilenberg cohomology for Hom-Lie algebras, we define Gerstenhaber bracket on the space of multilinear mappings of Hom-associative algebras and Nijenhuis-Richardson bracket on the space of multilinear mappings of Hom-Lie algebras. Also we enhance the deformations theory of this Hom-algebras by studying the obstructions.
The purpose of this paper is to study Hom-Lie superalgebras, that is a superspace with a bracket for which the superJacobi identity is twisted by a homomorphism. This class is a particular case of $Γ$-graded quasi-Lie algebras introduced by Larsson and Silvestrov. In this paper, we characterize Hom-Lie admissible superalgebras and provide a construction theorem from which we derive a one parameter family of Hom-Lie superalgebras deforming the orthosymplectic Lie superalgebra. Also, we prove a $\mathbb{Z}_2$-graded version of a Hartwig-Larsson-Silvestrov Theorem which leads us to a construction of a q-deformed Witt superalgebra.