On the structure of low-dimensional Leibniz algebras: some revision
Let \(L\) be an algebra over a field \(F\) with the binary operations \(+\) and \([\,\cdot\,{,}\,\cdot\,]\). Then \(L\) is called a left Leibniz algebra if \([[a,b],c]=[a,[b,c]]-[b,[a,c]]\) for all \(a,b,c\in L\). We describe the inner structure of left Leibniz algebras having dimension 3.
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| Datum: | 2023 |
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| Format: | Artikel |
| Sprache: | English |
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Lugansk National Taras Shevchenko University
2023
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2036 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-20362023-02-08T16:55:57Z On the structure of low-dimensional Leibniz algebras: some revision Kurdachenko, L. A. Pypka, O. O. Subbotin, I. Ya. Leibniz algebra, nilpotent Leibniz algebra, dimension 17A32, 17A60, 17A99 Let \(L\) be an algebra over a field \(F\) with the binary operations \(+\) and \([\,\cdot\,{,}\,\cdot\,]\). Then \(L\) is called a left Leibniz algebra if \([[a,b],c]=[a,[b,c]]-[b,[a,c]]\) for all \(a,b,c\in L\). We describe the inner structure of left Leibniz algebras having dimension 3. Lugansk National Taras Shevchenko University Isaac Newton Institute for Mathematical Sciences University of Edinburgh 2023-02-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2036 10.12958/adm2036 Algebra and Discrete Mathematics; Vol 34, No 1 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2036/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2036/1028 Copyright (c) 2023 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2023-02-08T16:55:57Z |
| collection |
OJS |
| language |
English |
| topic |
Leibniz algebra nilpotent Leibniz algebra dimension 17A32 17A60 17A99 |
| spellingShingle |
Leibniz algebra nilpotent Leibniz algebra dimension 17A32 17A60 17A99 Kurdachenko, L. A. Pypka, O. O. Subbotin, I. Ya. On the structure of low-dimensional Leibniz algebras: some revision |
| topic_facet |
Leibniz algebra nilpotent Leibniz algebra dimension 17A32 17A60 17A99 |
| format |
Article |
| author |
Kurdachenko, L. A. Pypka, O. O. Subbotin, I. Ya. |
| author_facet |
Kurdachenko, L. A. Pypka, O. O. Subbotin, I. Ya. |
| author_sort |
Kurdachenko, L. A. |
| title |
On the structure of low-dimensional Leibniz algebras: some revision |
| title_short |
On the structure of low-dimensional Leibniz algebras: some revision |
| title_full |
On the structure of low-dimensional Leibniz algebras: some revision |
| title_fullStr |
On the structure of low-dimensional Leibniz algebras: some revision |
| title_full_unstemmed |
On the structure of low-dimensional Leibniz algebras: some revision |
| title_sort |
on the structure of low-dimensional leibniz algebras: some revision |
| description |
Let \(L\) be an algebra over a field \(F\) with the binary operations \(+\) and \([\,\cdot\,{,}\,\cdot\,]\). Then \(L\) is called a left Leibniz algebra if \([[a,b],c]=[a,[b,c]]-[b,[a,c]]\) for all \(a,b,c\in L\). We describe the inner structure of left Leibniz algebras having dimension 3. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2036 |
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AT kurdachenkola onthestructureoflowdimensionalleibnizalgebrassomerevision AT pypkaoo onthestructureoflowdimensionalleibnizalgebrassomerevision AT subbotiniya onthestructureoflowdimensionalleibnizalgebrassomerevision |
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2025-12-02T15:44:16Z |
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2025-12-02T15:44:16Z |
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1850411850532913152 |