12 papers
Pseudo-Euclidean Novikov Superalgebras: Structure and Properties
Said Benayadi, Sofiane Bouarroudj, Hamza El Ouali
A pseudo-Euclidean Novikov superalgebra is a Novikov superalgebra endowed with a non-degenerate symmetric bilinear form such that all left multiplication oper…
Hyper relative differential operators on Lie algebras
Sofiane Bouarroudj, Jiefeng Liu, Liwen Zhang
In this paper, we first introduce the notion of a hyper relative differential operator on a Lie algebra, in which Nijenhuis operators are used to characterize the relative differen…
Computer-aided study of double extensions of restricted Lie superalgebras preserving the non-degenerate closed 2-forms in characteristic 2
Sofiane Bouarroudj, Dimitry Leites, Jin Shang
A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form is called a nis-(super)algebra. The double extension of a nis-(super)algebra $\mathf…
Structure of Flat Quadratic Quasi-Frobenius Lie Superalgebras via Double Extensions
Sofiane Bouarroudj, Hamza El Ouali
A flat quadratic quasi-Frobenius Lie superalgebra is a quadratic Lie superalgebra equipped with an additional symplectic structure that is flat with respect to the natural symplect…
Lagrangian extensions and left symmetric structures on the four-dimensional real Lie superalgebras
Sofiane Bouarroudj, Ana-Maria Radu
Over real numbers, Backhouse classified all four-dimensional Lie superalgebras. From this list, we will investigate those Lie superalgebras that can be obtained as Lagrangian exten…
Flat quasi-Frobenius Lie superalgebras
Sofiane Bouarroudj, Hamza El Ouali
A non-associative superalgebra is called pre-symplectic if it is equipped with a non-degenerate, anti-symmetric bilinear form. It is called quasi-Frobenius if, in addition, is a Li…