Crossed modules on leibniz algebras

In this thesis, we first determine some needed materials which will used in the sequel. Then we constructed an actor of a precat1-Leibniz algebra and give an actor of a precrossed module by using the isomorphism between the categories of precat1-Leibniz algebras and precrossed modules. By analogy with precrossed modules, we constructed an actor of a crossed module and gave a comparison between the actors of precrossed modules and crossed modules of Lie algebras and of Leibniz algebras. Finally, we looked some basic properties of nil(2) Leibniz algebras which have some similarities with precrossed modules.