On the Schur Lie-multiplier and Lie-covers of Leibniz n-algebras

被引：1
|
作者：
Safa, Hesam [1 ]
Biyogmam, Guy R. [2 ]
机构：
[1] Univ Bojnord, Fac Basic Sci, Dept Math, Bojnord 9453155111, Iran
[2] Georgia Coll & State Univ, Dept Math, Milledgeville, GA USA
来源：
COMMUNICATIONS IN ALGEBRA | 2023年 / 51卷 / 02期
关键词：
Leibniz n-algebra; Lie-cover; Schur Lie-multiplier; ISOCLINISM; CLASSIFICATION; DIMENSION; PAIR;
D O I：
10.1080/00927872.2022.2113400
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we study the notion of central extensions 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 and Green results on groups or Moneyhun results 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.
引用
收藏
页码：729 / 741
页数：13
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