Non-abelian tensor product of Leibniz algebras and an exact sequence in Leibniz homology

摘要

Let in and it be two-sided ideals of a Leibniz algebra g such that g = m + n. The goal of the paper is to achieve the exact sequence Ker(m(*)n + n(*)m --> g) --> HL2(q) --> HL2(g/m) circle plus HL2(g/n) --> m boolean AND n/ [m, n] --> HL1(g) --> HL1(g/m) circle plus HL1(g/n) --> 0, where HL* denotes the Leibniz homology with trivial coefficients of a Leibniz algebra and * denotes a non-abelian tensor product of Leibniz algebras. [References: 12]