A New Approach to Defining Cochain Complexes for dual Leibniz algebra

2025/12/22 by Hassan Alhussein, Alhussein, Hassan
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Advanced Combinatorial Mathematics

paper · doi:10.48550/arxiv.2512.19319

Abstract

We construct a cochain map embedding the cohomology complex of any dual Leibniz algebra B into the Lie algebra cochain complex of \mathfrakg ⊗ B, where \mathfrakg is a Leibniz algebra. This reduces the study of dual Leibniz cohomology to classical Lie algebra cohomology, yielding computational simplifications and new structural insights.

Citations

• Higher Jacobi identities
• Universal enveloping algebras of Leibniz algebras and (co)homology

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