On some non-nilpotent Leibniz algebras of dimension 3 and their automorphism groups
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 \(a,b,c\in L\). A linear transformation \(f\) of \(L\) is called an endomorphi...
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| Дата: | 2026 |
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| Автори та афіліації: |
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| Ключові слова: | keywords |
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| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2026
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2499 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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 \(a,b,c\in L\). 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 main goal of this article is to describe the structure of automorphism groups of certain types of non-nilpotent three-dimensional Leibniz algebras over an arbitrary field \(F\). |
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| DOI: | 10.12958/adm2499 |