30 citations · 84 across the 15 of their papers we have counts for
12 papers · 1 filter
Non-isomorphic restricted Lie algebras with isomorphic restricted enveloping algebras
Xabier García-Martínez
Let be a prime. For every field of characteristic we exhibit pairs of non-isomorphic finite-dimensional -nilpotent restricted Lie algebras and over whose…
A characterisation of Lie algebras using ideals and subalgebras
Vladimir Dotsenko, Xabier García-Martínez
We prove that if, for a nontrivial variety of non-associative algebras, every subalgebra of every free algebra is free and is an ideal whenever is an ideal, then this var…
On some properties of -centroids of Leibniz algebras
José Manuel Casas, Xabier García-Martínez, Natalia Pachego-Rego
We study some properties on -centroids related to central -derivations, generalized -derivations and almost inner -derivatio…
Actor of a crossed module of dialgebras via tetramultipliers
José Manuel Casas, Rafael Fernández-Casado, Xabier García-Martínez +1
We study the representability of actions in the category of crossed modules of dialgebras via tetramultipliers. We deduce a pair of dialgebras in order to construct an object which…
On the capablility of Hom-Lie algebras
José Manuel Casas, Xabier García-Martínez
A Hom-Lie algebra is said to be capable if there exists a Hom-Lie algebra such that . We obtain a characterisation of capable Hom-Lie algebras…
Abelian extensions and crossed modules of Hom-Lie algebras
José-Manuel Casas, Xabier García-Martínez
In this paper we study the low dimensional cohomology groups of Hom-Lie algebras and their relation with derivations, abelian extensions and crossed modules. On one hand, we introd…
A characterisation of Lie algebras amongst anti-commutative algebras
Xabier García-Martínez, Tim Van der Linden
Let be an infinite field. We prove that if a variety of anti-commutative -algebras - not necessarily associative, where is an identity - is locally…
A note on split extensions of bialgebras
Xabier García-Martínez, Tim Van der Linden
We prove a universal characterization of Hopf algebras among cocommutative bialgebras over a field: a cocommutative bialgebra is a Hopf algebra precisely when every split extension…
Actor of a crossed module of Leibniz algebras
José Manuel Casas, Rafael F. Casado, Xabier García-Martínez +1
We extend to the category of crossed modules of Leibniz algebras the notion of biderivation via the action of a Leibniz algebra. This results into a pair of Leibniz algebras which…
Universal central extensions of superdialgebras of matrices
Xabier García-Martínez, Manuel Ladra
We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of when and is a superdialgebr…
Non-abelian tensor product and homology of Lie Superalgebras
Xabier García-Martínez, Emzar Khmaladze, Manuel Ladra
We introduce the non-abelian tensor product of Lie superalgebras, study some of its properties including nilpotency, solvability and Engel, and we use it to describe the universal…
Universal central extensions of Lie-Rinehart algebras
José Luis Castiglioni, Xabier García-Martínez, Manuel Ladra
In this paper we study the universal central extension of a Lie--Rinehart algebra and we give a description of it. Then we study the lifting of automorphisms and derivations to cen…