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

页码：323 / 347

页数：25

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