A non-abelian exterior product and homology of Leibniz algebras

Abstract

We introduce a non-abelian exterior product of two crossed modules of Leibniz algebras and investigate its relation to the low-dimensional Leibniz homology. Later this non-abelian exterior product is applied to the construction of an eight term exact sequence in Leibniz homology. Also its relationship to the universal quadratic functor is established, which is applied to the comparison of the second Lie and Leibniz homologies of a Lie algebra.