On the structure of Leibniz algebras whose subalgebras are ideals or core-free

被引：0

作者：

Chupordia, V. A. ^{[1
]}

Kurdachenko, L. A. ^{[1
]}

Semko, N. N. ^{[2
]}

机构：

[1] Oles Honchar Dnipro Natl Univ, 72 Gagarin Ave, UA-49010 Dnipro, Ukraine

[2] Univ State Fiscal Serv Ukraine, 31 Univ Skaya Str, UA-08205 Irpin, Ukraine

来源：

ALGEBRA AND DISCRETE MATHEMATICS | 2020年 / 29卷 / 02期

关键词：

Leibniz algebra; Lie algebra; ideal; core-free subalgebras; monolithic algebra; extraspecial algebra; CENTRAL SERIES;

D O I：

10.12958/adm1533

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An algebra L over a field F is said to be a Leibniz algebra (more precisely, a left Leibniz algebra) if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] - [b, [a, c]] for all a, b, c is an element of L. Leibniz algebras are generalizations of Lie algebras. A subalgebra S of a Leibniz algebra L is called a core-free, if S does not include a non-zero ideal. We study the Leibniz algebras, whose subalgebras are either ideals or core-free.

引用

页码：180 / 194

页数：15

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