Non-abelian Tensor Product of Leibniz Algebras and an Exact Sequence in Leibniz Homology
J. M. CasasDepartamento Matemática Aplicada , Universidad de Vigo , Pontevedra, Spain ; Departamento Matemática Aplicada , Universidad de Vigo, E. U. I. T. Forestal, Campus Universitario A Xunqueira , Pontevedra, 36005, SpainM. LadraDepartamento de Algebra , Universidad de Santiago , Santiago de Compostela, Spain ; Departamento de Algebra , Universidad de Santiago , Santiago de Compostela, 15782, Spain
2003en
ABI
Аннотация
Abstract Let 𝔪 and 𝔫 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) → HL 2(𝔤) → HL 2(𝔤/𝔪) ⊕ HL 2(𝔤/𝔫) → 𝔪 ∩ 𝔫/ [𝔪,𝔫] → HL 1(𝔤) → HL 1(𝔤/𝔪) ⊕ HL 1(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.
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