Low-dimensional nilpotent Leibniz algebras and their automorphism groups

Low-dimensional nilpotent Leibniz algebras and their automorphism groups

Let \(L\) be an algebra over a field \(F\) with the binary operations \(+\) and \([,]\). Then \(L\) is called a Leibniz algebra if it satisfies the Leibniz identity: \([a,[b,c]]=[[a,b],c]+[b,[a,c]]\) for all \(a,b,c\in L\). A linear transformation \(f\) of \(L\) is called an endomorphism of \(L\), i...

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Date:2024
Main Authors: Minaiev, Pavlo Ye., Pypka, Oleksandr O., Semko, Larysa P.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2024
Subjects:
Leibniz algebra
automorphism group
17A32
17A36
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2264
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-2264
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spelling oai:ojs.admjournal.luguniv.edu.ua:article-22642024-06-27T08:42:43Z Low-dimensional nilpotent Leibniz algebras and their automorphism groups Minaiev, Pavlo Ye. Pypka, Oleksandr O. Semko, Larysa P. Leibniz algebra, automorphism group 17A32, 17A36 Let \(L\) be an algebra over a field \(F\) with the binary operations \(+\) and \([,]\). Then \(L\) is called a Leibniz algebra if it satisfies the Leibniz identity: \([a,[b,c]]=[[a,b],c]+[b,[a,c]]\) for all \(a,b,c\in L\). A linear transformation \(f\) of \(L\) is called an endomorphism of \(L\), if \(f([a,b])=[f(a),f(b)]\) for all \(a,b\in L\). A bijective endomorphism of \(L\) is called an automorphism of \(L\). The set of all automorphisms of Leibniz algebra is a group with respect to the operation of multiplication of automorphisms. 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 over arbitrary field \(F\). Lugansk National Taras Shevchenko University 2024-06-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2264 10.12958/adm2264 Algebra and Discrete Mathematics; Vol 37, No 2 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2264/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2264/1184 Copyright (c) 2024 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2024-06-27T08:42:43Z
collection OJS
language English
topic Leibniz algebra
automorphism group
17A32
17A36
spellingShingle Leibniz algebra
automorphism group
17A32
17A36
Minaiev, Pavlo Ye.
Pypka, Oleksandr O.
Semko, Larysa P.
Low-dimensional nilpotent Leibniz algebras and their automorphism groups
topic_facet Leibniz algebra
automorphism group
17A32
17A36
format Article
author Minaiev, Pavlo Ye.
Pypka, Oleksandr O.
Semko, Larysa P.
author_facet Minaiev, Pavlo Ye.
Pypka, Oleksandr O.
Semko, Larysa P.
author_sort Minaiev, Pavlo Ye.
title Low-dimensional nilpotent Leibniz algebras and their automorphism groups
title_short Low-dimensional nilpotent Leibniz algebras and their automorphism groups
title_full Low-dimensional nilpotent Leibniz algebras and their automorphism groups
title_fullStr Low-dimensional nilpotent Leibniz algebras and their automorphism groups
title_full_unstemmed Low-dimensional nilpotent Leibniz algebras and their automorphism groups
title_sort low-dimensional nilpotent leibniz algebras and their automorphism groups
description Let \(L\) be an algebra over a field \(F\) with the binary operations \(+\) and \([,]\). Then \(L\) is called a Leibniz algebra if it satisfies the Leibniz identity: \([a,[b,c]]=[[a,b],c]+[b,[a,c]]\) for all \(a,b,c\in L\). A linear transformation \(f\) of \(L\) is called an endomorphism of \(L\), if \(f([a,b])=[f(a),f(b)]\) for all \(a,b\in L\). A bijective endomorphism of \(L\) is called an automorphism of \(L\). The set of all automorphisms of Leibniz algebra is a group with respect to the operation of multiplication of automorphisms. 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 over arbitrary field \(F\).
publisher Lugansk National Taras Shevchenko University
publishDate 2024
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2264
work_keys_str_mv AT minaievpavloye lowdimensionalnilpotentleibnizalgebrasandtheirautomorphismgroups
AT pypkaoleksandro lowdimensionalnilpotentleibnizalgebrasandtheirautomorphismgroups
AT semkolarysap lowdimensionalnilpotentleibnizalgebrasandtheirautomorphismgroups
first_indexed 2025-07-17T10:35:22Z
last_indexed 2025-07-17T10:35:22Z
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