Description of the automorphism groups of some Leibniz algebras
Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ 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 $a,b,c\in L$. A linear transformation $f$ of $L$ is called an endomorphism of $L$, if...
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| Format: | Article |
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Oles Honchar Dnipro National University
2023-06-01
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| Series: | Researches in Mathematics |
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| Online Access: | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/399/399 |
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| author | L.A. Kurdachenko O.O. Pypka M.M. Semko |
| author_facet | L.A. Kurdachenko O.O. Pypka M.M. Semko |
| author_sort | L.A. Kurdachenko |
| collection | DOAJ |
| description | Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ 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 $a,b,c\in L$. A linear transformation $f$ of $L$ is called an endomorphism of $L$, if $f([a,b])=[f(a),f(b)]$ for all elements $a,b\in L$. A bijective endomorphism of $L$ is called an automorphism of $L$. It is easy to show that the set of all automorphisms of the Leibniz algebra is a group with respect to the operation of multiplication of automorphisms. The description of the structure of the automorphism groups of Leibniz algebras is one of the natural and important problems of the general Leibniz algebra theory. The main goal of this article is to describe the structure of the automorphism group of a certain type of nilpotent three-dimensional Leibniz algebras. |
| first_indexed | 2024-03-13T04:30:44Z |
| format | Article |
| id | doaj.art-320e2dee4aed4006a9bdeb0f4777af66 |
| institution | Directory Open Access Journal |
| issn | 2664-4991 2664-5009 |
| language | English |
| last_indexed | 2024-03-13T04:30:44Z |
| publishDate | 2023-06-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Researches in Mathematics |
| spelling | doaj.art-320e2dee4aed4006a9bdeb0f4777af662023-06-19T14:01:15ZengOles Honchar Dnipro National UniversityResearches in Mathematics2664-49912664-50092023-06-01311526110.15421/242305Description of the automorphism groups of some Leibniz algebrasL.A. Kurdachenko0https://orcid.org/0000-0002-6368-7319O.O. Pypka1https://orcid.org/0000-0003-0837-5395M.M. Semko2https://orcid.org/0000-0003-0123-4872Oles Honchar Dnipro National UniversityOles Honchar Dnipro National UniversityState Tax UniversityLet $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ 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 $a,b,c\in L$. A linear transformation $f$ of $L$ is called an endomorphism of $L$, if $f([a,b])=[f(a),f(b)]$ for all elements $a,b\in L$. A bijective endomorphism of $L$ is called an automorphism of $L$. It is easy to show that the set of all automorphisms of the Leibniz algebra is a group with respect to the operation of multiplication of automorphisms. The description of the structure of the automorphism groups of Leibniz algebras is one of the natural and important problems of the general Leibniz algebra theory. The main goal of this article is to describe the structure of the automorphism group of a certain type of nilpotent three-dimensional Leibniz algebras.https://vestnmath.dnu.dp.ua/index.php/rim/article/view/399/399leibniz algebraautomorphism group |
| spellingShingle | L.A. Kurdachenko O.O. Pypka M.M. Semko Description of the automorphism groups of some Leibniz algebras Researches in Mathematics leibniz algebra automorphism group |
| title | Description of the automorphism groups of some Leibniz algebras |
| title_full | Description of the automorphism groups of some Leibniz algebras |
| title_fullStr | Description of the automorphism groups of some Leibniz algebras |
| title_full_unstemmed | Description of the automorphism groups of some Leibniz algebras |
| title_short | Description of the automorphism groups of some Leibniz algebras |
| title_sort | description of the automorphism groups of some leibniz algebras |
| topic | leibniz algebra automorphism group |
| url | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/399/399 |
| work_keys_str_mv | AT lakurdachenko descriptionoftheautomorphismgroupsofsomeleibnizalgebras AT oopypka descriptionoftheautomorphismgroupsofsomeleibnizalgebras AT mmsemko descriptionoftheautomorphismgroupsofsomeleibnizalgebras |