On complete Leibniz algebras

被引：4

作者：

Ayupov, Sh A. ^{[1
,2
]}

Khudoyberdiyev, A. Kh ^{[1
,2
]}

Shermatova, Z. Kh ^{[1
]}

机构：

[1] Uzbek Acad Sci, VI Romanovskiy Inst Math, Univ St 9, Tashkent 100174, Uzbekistan

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

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2022年 / 32卷 / 02期

关键词：

Leibniz algebra; complete algebra; semisimple algebra; solvability; radical; nilradical; derivation; outer derivation; CLASSIFICATION;

D O I：

10.1142/S0218196722500138

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to the so-called complete Leibniz algebras. We construct some complete Leibniz algebras with complete radical and prove that the direct sum of complete Leibniz algebras is also complete. It is known that a Lie algebra with a complete ideal is split. We discuss the analogs of this result for the Leibniz algebras and show that it is true for some special classes of Leibniz algebras. Finally, we consider derivations of Leibniz algebras and present some classes of Leibniz algebras which are not complete, since they admit outer derivation.

引用

页码：265 / 288

页数：24

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