On the structure of automorphism groups of some low-dimensional Leibniz algebras
UDC 512.554 Let $L$ be an algebra over a field $F$ with binary operations $+$ and $[,]$. $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. We study he structure of the  group of aut...
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| Date: | 2024 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Ukrainian |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7868 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512794030374912 |
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| author | Kurdachenko, L. Pypka, O. Semko, M. Курдаченко, Леонід Пипка, Олександр Семко, Микола |
| author_facet | Kurdachenko, L. Pypka, O. Semko, M. Курдаченко, Леонід Пипка, Олександр Семко, Микола |
| author_sort | Kurdachenko, L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-07-15T03:05:06Z |
| description | UDC 512.554
Let $L$ be an algebra over a field $F$ with binary operations $+$ and $[,]$. $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. We study he structure of the  group of automorphisms of $3$-dimensional Leibniz algebras with nilpotency class $2$ and a one-dimensional center. |
| doi_str_mv | 10.3842/umzh.v76i5.7868 |
| first_indexed | 2026-03-24T03:34:26Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-7868 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T03:34:26Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ea/cacf019b22db6975a779ce7ac232c6ea |
| spelling | umjimathkievua-article-78682024-07-15T03:05:06Z On the structure of automorphism groups of some low-dimensional Leibniz algebras Про будову груп автоморфізмів деяких алгебр Лейбніца малої вимірності Kurdachenko, L. Pypka, O. Semko, M. Курдаченко, Леонід Пипка, Олександр Семко, Микола Leibniz algebra automorphism group алгебра Лейбніца група автоморфізмів UDC 512.554 Let $L$ be an algebra over a field $F$ with binary operations $+$ and $[,]$. $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. We study he structure of the  group of automorphisms of $3$-dimensional Leibniz algebras with nilpotency class $2$ and a one-dimensional center. УДК 512.554 Нехай $L$ — алгебра над полем $F$ з бінарними операціями $+$ та $[,].$ $L$ називатимемо лівою алгеброю Лейбніца, якщо вона задовольняє ліву тотожність Лейбніца: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ для всіх елементів $a,b,c\in L.$ Досліджено будову групи автоморфізмів $3$-вимірних алгебр Лейбніца, які мають клас нільпотентності $2$ та центр розмірності $1.$ Institute of Mathematics, NAS of Ukraine 2024-07-03 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7868 10.3842/umzh.v76i5.7868 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 6 (2024); 864–876 Український математичний журнал; Том 76 № 6 (2024); 864–876 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/7868/10033 Copyright (c) 2024 Oleksandr Pypka |
| spellingShingle | Kurdachenko, L. Pypka, O. Semko, M. Курдаченко, Леонід Пипка, Олександр Семко, Микола On the structure of automorphism groups of some low-dimensional Leibniz algebras |
| title | On the structure of automorphism groups of some low-dimensional Leibniz algebras |
| title_alt | Про будову груп автоморфізмів деяких алгебр Лейбніца малої вимірності |
| title_full | On the structure of automorphism groups of some low-dimensional Leibniz algebras |
| title_fullStr | On the structure of automorphism groups of some low-dimensional Leibniz algebras |
| title_full_unstemmed | On the structure of automorphism groups of some low-dimensional Leibniz algebras |
| title_short | On the structure of automorphism groups of some low-dimensional Leibniz algebras |
| title_sort | on the structure of automorphism groups of some low-dimensional leibniz algebras |
| topic_facet | Leibniz algebra automorphism group алгебра Лейбніца група автоморфізмів |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7868 |
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