4 papers
A non-abelian exterior product and homology of Leibniz algebras
Guram Donadze, Xabier García-Martínez, Emzar Khmaladze
We introduce a non-abelian exterior product of two crossed modules of Leibniz algebra and investigate its relation to the low dimensional Leibniz homology. Later this non-abelian e…
A new characterisation of groups amongst monoids
Xabier García-Martínez
We prove that a monoid is a group if and only if, in the category of monoids, all points over are strong. This sharpens and greatly simplifies a result of Montoli, Rodelo a…
A natural extension of the universal enveloping algebra functor to crossed modules of Leibniz algebras
Rafael F. Casado, Xabier García-Martínez, Manuel Ladra
The universal enveloping algebra functor between Leibniz and associative algebras defined by Loday and Pirashvili is extended to crossed modules. We prove that the universal envelo…
Do -Lie algebras have universal enveloping algebras
Xabier Garcia-Martinez, Rustam Turdibaev, Tim van der Linden
The aim of this paper is to investigate in which sense, for , -Lie algebras admit universal enveloping algebras. There have been some attempts at a construction (see [1…