2020/04/28 by Hesam Safa, Safa, Hesam, Guy Roger Biyogmam +1
Mathematics · #17A32 #18B99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2004.13658
openalex publication_date 2020/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we study the notion of central extension of Leibniz n-algebras relative to n-Lie algebras to study properties of Schur Lie-multiplier and Lie-covers on Leibniz n-algebras. We provide a characterization of Lie-perfect Leibniz n-algebras by means of universal Lie-central extensions. It is also provided some inequalities on the dimension of the Schur Lie-multiplier of Leibniz n-algebras. Analogue to Wiegold [38] and Green [17] results on groups or Moneyhun [26] result on Lie algebras, we provide upper bounds for the dimension of the Lie-commutator of a Leibniz n-algebra with finite dimensional Lie-central factor, and also for the dimension of the Schur Lie-multiplier of a finite dimensional Leibniz n-algebra.