5 papers
Cyclic Riemannian Lie groups: description and curvatures
Fatima-Ezzahrae Abid, Said Benayadi, Mohamed Boucetta +2
A cyclic Riemannian Lie group is a Lie group equipped with a left-invariant Riemannian metric that satisfies for any left-invariant vector field…
Symplectic Leibniz algebras as a non-commutative version of symplectic Lie algebras
Fatima-Ezzahrae Abid, Mohamed Boucetta
We introduce symplectic left Leibniz algebras and symplectic right Leibniz algebras as generalizations of symplectic Lie algebras. These algebras possess a left symmetric product a…
Complete Description of Invariant, Associative Pseudo-Euclidean Metrics on Left Leibniz Algebras via Quadratic Lie Algebras
Fatima-Ezzahrae Abid, Mohamed Boucetta
A pseudo-Euclidean non-associative algebra is a real algebra of finite dimension that has a metric, i.e., a bilinear, symmetric, and non-degenerate form $…
A class of Lie racks associated to symmetric Leibniz algebras
Abchir Hamid, Fatima-Ezzahrae Abid, Mohamed Boucetta
Given a symmetric Leibniz algebra , the product is Lie-admissible and defines a Lie algebra bracket on . Let be the connected and simply…
Analytic Linear Lie rack Structures on Leibniz Algebras
Hamid Abchir, Fatima-Ezzahrae Abid, Mohamed Boucetta
A linear Lie rack structure on a finite dimensional vector space is a Lie rack operation pointed at the origin and such that for any , the left transl…