Local and 2-Local Derivations and Automorphisms on Simple Leibniz Algebras

被引：26

作者：

Ayupov, Shavkat ^{[1
]}

Kudaybergenov, Karimbergen ^{[2
]}

Omirov, Bakhrom ^{[3
]}

机构：

[1] Uzbek Acad Sci, VI Romanovskiy Inst Math, 81 Mirzo Ulughbek St, Tashkent 100170, Uzbekistan

[2] Karakalpak State Univ, Dept Math, Ch Abdirov 1, Nukus 230113, Uzbekistan

[3] Natl Univ Uzbekistan, 4 Univ St, Tashkent 100174, Uzbekistan

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2020年 / 43卷 / 03期

关键词：

Simple Leibniz algebra; Derivation; Automorphism; NILPOTENT;

D O I：

10.1007/s40840-019-00799-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to study local and 2-local derivations and automorphism of complex finite-dimensional simple Leibniz algebras. We show that all local derivations and 2-local derivations on a finite-dimensional complex simple Leibniz algebra are automatically derivations. We prove that nilpotent Leibniz algebras as a rule admit local derivations and 2-local derivations which are not derivations. Further, we consider automorphisms of simple Leibniz algebras. It is established that every 2-local automorphism on a complex finite-dimensional simple Leibniz algebra is an automorphism and that nilpotent Leibniz algebras admit 2-local automorphisms which are not automorphisms. A similar problem concerning local automorphism on simple Leibniz algebras is reduced to the case of simple Lie algebras.

引用

页码：2199 / 2234

页数：36

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