Central extensions of null-filiform and naturally graded filiform non-Lie Leibniz algebras

被引：29
|
作者：
Adashev, J. K. [1 ]
Camacho, L. M. [2 ]
Omirov, B. A. [1 ]
机构：
[1] Natl Univ Uzbekistan, Inst Math, Tashkent 100125, Uzbekistan
[2] Univ Seville, Dept Matemat Aplicada 1, Avda Reina Mercedes S-N, E-41012 Seville, Spain
来源：
JOURNAL OF ALGEBRA | 2017年 / 479卷
关键词：
Leibniz algebra; Filiform algebra; Quasi-filiform algebra; Natural gradation; Characteristic sequence; 2-cocycles; Central extension;
D O I：
10.1016/j.jalgebra.2017.02.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we describe central extensions of some nilpotent Leibniz algebras. Namely, central extensions of the Leibniz algebra with maximal index of nilpotency are classified. Moreover, non-split central extensions of naturally graded filiform non-Lie Leibniz algebras are described up to isomorphism. It is shown that k-dimensional central extensions (k >= 5) of these algebras are split. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：461 / 486
页数：26
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