7 papers
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…
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…
Quadratic symplectic Lie superalgebras over filiform modules
Elisabete Barreiro, Saïd Benayadi, Rosa M. Navarro +1
The present work studies deeply quadratic symplectic Lie superalgebras, obtaining, in particular, that they are all nilpotent. Consequently, we provide classifications in low dimen…
On split regular Hom-Lie superalgebras
Helena Albuquerque, Elisabete Barreiro, Antonio J. Calderón +1
We introduce the class of split regular Hom-Lie superalgebras as the natural extension of the one of split Hom-Lie algebras and Lie superalgebras, and study its structure by showin…
Leibniz algebras and graphs
Elisabete Barreiro, Antonio J. Calderón, Samuel Lopes +1
We consider a Leibniz algebra over an arbitrary base field , being the ideal generated by the produ…
Odd-quadratic Lie superalgebras with a weak filiform module as an odd part
Elisabete Barreiro, Saïd Benayadi, Rosa M. Navarro +1
The aim of this work is to study a very special family of odd-quadratic Lie superalgebras such that ${\mathfrak…