54 citations · 273 across the 53 of their papers we have counts for
34 papers · 1 filter
The Superization of Hochschild's Lemma and Restricted Lie-Rinehart Superalgebras
Sofiane Bouarroudj, Quentin Ehret, Abdenacer Makhlouf +1
The main goal of this paper is to introduce the notion of restricted Lie-Rinehart superalgebra over a field of characteristic , motivated by a generalization of Hochschild's l…
Cohomology of Restricted Poisson algebras in characteristic 2
Sofiane Bouarroudj, Quentin Ehret, Jiefeng Liu
In this paper, we study restricted Poisson algebras in characteristic 2 and their relationship with restricted Lie-Rinehart algebras, for which we develop a cohomology theory and i…
Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2
Saïd Benayadi, Sofiane Bouarroudj, Quentin Ehret
The purpose of this paper is twofold. First, we introduce the notions of left-symmetric and left alternative structures on superspaces in characteristic 2. We describe their main p…
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…
Double extensions of quasi-Frobenius Lie superalgebras with degenerate center
Sofiane Bouarroudj, Quentin Ehret
We develop the process of symplectic double extensions for Lie superalgebras with degenerate center. The construction is a superization of a recent work by Fischer, and generalize…
Central extensions of restricted Lie superalgebras and classification of -nilpotent Lie superalgebras in dimension
Sofiane Bouarroudj, Quentin Ehret
The first main result of this paper is to build the first and second restricted cohomology groups for restricted Lie superalgebras in characteristic , modifying a construct…
Symplectic Double Extensions for Restricted Quasi-Frobenius Lie (Super)Algebras
Sofiane Bouarroudj, Quentin Ehret, Yoshiaki Maeda
In this paper, we present a method of symplectic double extensions for restricted quasi-Frobenius Lie superalgebras. Certain cocycles in the restricted cohomology represent obstruc…
Hom-Lie superalgebras in characteristic 2
Sofiane Bouarroudj, Abdenacer Makhlouf
The main goal of this paper is to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, -derivations…
Analogs of Bol operators for
Sofiane Bouarroudj, Dimitry Leites, Irina Shchepochkina
Bol operators (Bols for short) are differential operators invariant under the projective action of between spaces of weighted densities on…
Analogs of Bol operators on superstrings
Sofiane Bouarroudj, Dimitry Leites, Irina Shchepochkina
The Bol operators are unary differential operators between spaces of weighted densities on the 1-dimensional manifold invariant under projective transformations of the manifold. On…
Double and Lagrangian extensions for quasi-Frobenius Lie superalgebras
Sofiane Bouarroudj, Yoshiaki Maeda
A Lie superalgebra is called quasi-Frobenius if it admits a closed anti-symmetric non-degenerate bilinear form. We study the notion of double extensions of quasi-Frobenius Lie supe…
Manin triples and non-degenerate anti-symmetric bilinear forms on Lie superalgebras in characteristic
Said Benayadi, Sofiane Bouarroudj
In this paper, we introduce and develop the notion of a Manin triple for a Lie superalgebra defined over a field of characteristic . We find cohomological necess…
Cohomologically rigid solvable Lie superalgebras with model filiform and model nilpotent nilradical
S. Bouarroudj, R. M. Navarro
In this paper, we find a family , in any arbitrary dimensions, of cohomologically rigid solvable Lie superalgebras with nilradical the model filiform Lie superalgebra $L^…
The roots of exceptional modular Lie superalgebras with Cartan matrix
Sofiane Bouarroudj, Dimitry Leites, Alexander Lozhechnyk +1
For each of the exceptional Lie superalgebras with indecomposable Cartan matrix, we give the explicit list of its roots of and the corresponding Chevalley basis for one of the ineq…
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…
Double extensions of restricted Lie (super)algebras
Said Benayadi, Sofiane Bouarroudj, Mounir Hajli
A double extension ( extension) of a Lie (super)algebra with a non-degenerate invariant symmetric bilinear form , briefly: a NIS-(super)alge…
Restricted simple Lie (super)algebras in characteristic
Sofiane Bouarroudj, Andrey Krutov, Alexei Lebedev +2
We give explicit formulas proving restrictedness of the following Lie (super)algebras: known exceptional simple vectorial Lie (super)algebras in characteristic 3, deformed Lie (sup…
Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras
Sofiane Bouarroudj, Andrey Krutov, Dimitry Leites +1
We review the list of non-degenerate invariant (super)symmetric bilinear forms (briefly: NIS) on the following simple (relatives of) Lie (super)algebras: (a) with symmetrizable Car…
Double extensions of Lie superalgebras in characteristic 2 with nondegenerate invariant supersymmetric bilinear form
Said Benayadi, Sofiane Bouarroudj
A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form will be called a NIS-Lie (super)algebra. The double extension of a NIS-Lie (super)algebra is the result…
Invariant differential operators in positive characteristic
Sofiane Bouarroudj, Dimitry Leites
We consider an analog of the problem Veblen formulated in 1928 at the IMC: classify invariant differential operators between "natural objects" (spaces of either tensor fields, or j…
Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations
Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev +2
We overview the classifications of simple finite-dimensional modular Lie algebras. In characteristic 2, their list is wider than that in other characteristics; e.g., it contains de…
Classification of simple Lie superalgebras in characteristic
Sofiane Bouarroudj, Alexei Lebedev, Dimitry Leites +1
All results concern characteristic 2. Two procedures that to every simple Lie algebra assign simple Lie superalgebras, most of the latter new, are offered. We prove that every simp…
Simple prolongs of the non-positive parts of graded Lie algebras with Cartan matrix in characteristic 2
Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev +2
Over an algebraically closed fields, an alternative to the method due to Kostrikin and Shafarevich was recently suggested. It produces all known simple finite dimensional Lie algeb…
Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras
Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev +1
Over algebraically closed fields of positive characteristic, for simple Lie (super)algebras, and certain Lie (super)algebras close to simple ones, with symmetric root systems (such…