6 papers · 1 filter
Pre-symplectic left-symmetric algebras
Saïd Benayadi, Hamza El Ouali
A pre-symplectic left-symmetric algebra is a left-symmetric algebra endowed with a nondegenerate skew-symmetric bilinear form such that all left multiplication op…
On anti-left-invariant and left-invariant pseudo-Euclidean nearly associative algebras
Elisabete Barreiro, Said Benayadi, Hamza El Ouali +1
We introduce the notions of anti-left-invariant and left-invariant pseudo-Euclidean nearly associative algebras, which arise as nearly associative Levi-Civita products associated w…
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…
Flat pseudo-Euclidean Leibniz superalgebras
Saïd Benayadi, Sofiane Bouarroudj, Hamza El Ouali
In this paper, we introduce pre-Lie and pre-Leibniz superalgebras, which generalize pre-Lie and pre-Leibniz algebras to the super setting. Additionally, we define a Levi-Civita pro…
Nonassociative algebras of anti-biderivation-type
Saïd Benayadi, Said Boulmane, Ivan Kaygorodov
The main purpose of this paper is to study the class of Jacobi-Jordan-admissible algebras, such that its product is an anti-biderivation of the related Jacobi-Jordan algebra. We ca…
Bialgebra theory for nearly associative algebras and -algebras: equivalence, characterization, and -Yang-Baxter Equation
Elisabete Barreiro, Saïd Benayadi, Carla Rizzo
We develop the bialgebra theory for two classes of non-associative algebras: nearly associative algebras and -algebras. In particular, building on recent studies that reveal co…