Locally Nilpotent Derivations of Free Algebra of Rank Two
In commutative algebra, if δ is a locally nilpotent derivation of the polynomial algebra 𝛫[x₁, …, xd] over a field 𝛫 of characteristic 0 and w is a nonzero element of the kernel of δ, then Δ=wδ is also a locally nilpotent derivation with the same kernel as δ. In this paper, we prove that the locally...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210297 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Locally Nilpotent Derivations of Free Algebra of Rank Two / V. Drensky, L. Makar-Limanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 31 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | In commutative algebra, if δ is a locally nilpotent derivation of the polynomial algebra 𝛫[x₁, …, xd] over a field 𝛫 of characteristic 0 and w is a nonzero element of the kernel of δ, then Δ=wδ is also a locally nilpotent derivation with the same kernel as δ. In this paper, we prove that the locally nilpotent derivation Δ of the free associative algebra 𝛫⟨X, Y⟩ is determined up to a multiplicative constant by its kernel. We also show that the kernel of Δ is a free associative algebra and give an explicit set of its free generators.
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| ISSN: | 1815-0659 |