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

TitleOn the structure of Leibniz algebras, whose subalgebras are ideals or core-free
Publication TypeJournal Article
Year of Publication2020
AuthorsChupordia, VA, Kurdachenko, LA, Semko, NN
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2020.07.017
Issue7
SectionMathematics
Pagination17-21
Date Published7/2020
LanguageEnglish
Abstract

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 ∈ L. Leibniz algebras are generalizations of Lie algebras. A subalgebra S of a Leibniz algebra L is called core-free, if S does not include the non-zero ideal. We study the Leibniz algebras, whose subalgebras are either ideals or core-free.

Keywordscore-free subalgebras, extraspecial algebra, ideal, Leibniz algebra, Lie algebra, monolithic algebra
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