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arXiv · 2004.13658

On the Schur $\mathsf{Lie}$-multiplier and $\mathsf{Lie}$-covers of Leibniz $n$-algebras

Hesam Safa·Guy R. Biyogmam
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Abstract

In this article, we study the notion of central extension of Leibniz $n$-algebras relative to $n$-Lie algebras to study properties of Schur $\mathsf{Lie}$-multiplier and $\mathsf{Lie}$-covers on Leibniz $n$-algebras. We provide a characterization of $\mathsf{Lie}$-perfect Leibniz $n$-algebras by means of universal $\mathsf{Lie}$-central extensions. It is also provided some inequalities on the dimension of the Schur $\mathsf{Lie}$-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 $\mathsf{Lie}$-commutator of a Leibniz $n$-algebra with finite dimensional $\mathsf{Lie}$-central factor, and also for the dimension of the Schur $\mathsf{Lie}$-multiplier of a finite dimensional Leibniz $n$-algebra.

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BibTeXRIS

Hesam Safa, Guy R. Biyogmam. 2020-04-28. On the Schur $\mathsf{Lie}$-multiplier and $\mathsf{Lie}$-covers of Leibniz $n$-algebras. https://arxiv.org/abs/2004.13658

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