On the structure of Leibniz algebras whose subalgebras are ideals or core-free
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 \(a, b, c \in L\). Leibniz algebras are generalizations of Lie algebras. A subalgebra \(S\) of a Leib...
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Lugansk National Taras Shevchenko University
2020
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oai:ojs.admjournal.luguniv.edu.ua:article-15332020-07-08T07:13:20Z On the structure of Leibniz algebras whose subalgebras are ideals or core-free Chupordia, V. A. Kurdachenko, L. A. Semko, N. N. 17A32, 17A60, 17A99 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 \(a, b, c \in L\). 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. Lugansk National Taras Shevchenko University Leibniz algebra, Lie algebra, ideal, core-free subalgebras, monolithic algebra, extraspecial algebra 2020-07-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1533 10.12958/adm1533 Algebra and Discrete Mathematics; Vol 29, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1533/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1533/659 Copyright (c) 2020 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2020-07-08T07:13:20Z |
| collection |
OJS |
| language |
English |
| topic |
17A32 17A60 17A99 |
| spellingShingle |
17A32 17A60 17A99 Chupordia, V. A. Kurdachenko, L. A. Semko, N. N. On the structure of Leibniz algebras whose subalgebras are ideals or core-free |
| topic_facet |
17A32 17A60 17A99 |
| format |
Article |
| author |
Chupordia, V. A. Kurdachenko, L. A. Semko, N. N. |
| author_facet |
Chupordia, V. A. Kurdachenko, L. A. Semko, N. N. |
| author_sort |
Chupordia, V. A. |
| title |
On the structure of Leibniz algebras whose subalgebras are ideals or core-free |
| title_short |
On the structure of Leibniz algebras whose subalgebras are ideals or core-free |
| title_full |
On the structure of Leibniz algebras whose subalgebras are ideals or core-free |
| title_fullStr |
On the structure of Leibniz algebras whose subalgebras are ideals or core-free |
| title_full_unstemmed |
On the structure of Leibniz algebras whose subalgebras are ideals or core-free |
| title_sort |
on the structure of leibniz algebras whose subalgebras are ideals or core-free |
| description |
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 \(a, b, c \in L\). 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1533 |
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| first_indexed |
2025-07-17T10:31:56Z |
| last_indexed |
2025-07-17T10:31:56Z |
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1837889818778927104 |