论文标题
在Schur $ \ Mathsf {Lie} $ - 乘数和$ \ Mathsf {Lie} $ - Leibniz $ N $ -Algebras的封面
On the Schur $\mathsf{Lie}$-multiplier and $\mathsf{Lie}$-covers of Leibniz $n$-algebras
论文作者
论文摘要
在本文中，我们研究了Leibniz $ n $代数相对于$ n $ -lie代数的中心扩展的概念，以研究Schur $ \ Mathsf {Lie} $的属性 - 乘数和$ \ Mathsf {lie} $ - 覆盖Leibniz $ n $ algebras。我们通过通用$ \ mathsf {lie} $ - 中央扩展名提供了$ \ mathsf {lie} $的特征 - 完美的leibniz $ n $ -algebras。还提供了有关Schur $ \ Mathsf {lie} $的尺寸的一些不等式 - Leibniz $ n $ -algebras的乘数。对Wiegold [38]和Green [17]的类似物或Moneyhun [26]的结果是谎言代数，我们为$ \ \ m athsf {lie} $的维度提供了上限 - leibniz $ n $ n $ n $ -algebra具有有限尺寸的liibniz $ n $ algebra的换算器$ \ mathsf {lie} $ - 有限尺寸leibniz $ n $ -algebra的乘数。
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.
