A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations

被引：14
|
作者：
Kaygorodov, Ivan [1 ,2 ,3 ]
Popov, Yu. [3 ,4 ]
机构：
[1] Univ Fed ABC, CMCC, Santo Andre, Brazil
[2] Univ Sao Paulo, BR-05508 Sao Paulo, Brazil
[3] Sobolev Inst Math, Novosibirsk, Russia
[4] Novosibirsk State Univ, Novosibirsk, Russia
来源：
JOURNAL OF ALGEBRA | 2016年 / 456卷
基金：
巴西圣保罗研究基金会;
关键词：
Leibniz derivation; Malcev algebra; Jordan algebra; (-1,1)-Algebra; Nilpotent algebra; LIE-ALGEBRAS; NONSINGULAR DERIVATIONS; GENERALIZED DERIVATIONS; P-GROUPS; ORDERS; PREDERIVATIONS;
D O I：
10.1016/j.jalgebra.2016.02.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Moens proved that a finite-dimensional Lie algebra over a field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation. In this article we prove the analogous results for finite-dimensional Malcev, Jordan, (-1,1)-, right alternative, Zinbiel and Malcev-admissible noncommutative Jordan algebras over a field of characteristic zero. Also, we describe all Leibniz-derivations of semisimple Jordan, right alternative and Malcev algebras. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：323 / 347
页数：25
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