Finite-dimensional subalgebras in polynomial Lie algebras of rank one
Let $W_n(\mathbb{K})$ be the Lie algebra of derivations of the polynomial algebra $\mathbb{K}[X] := \mathbb{K}[x_1,... ,x_n]$ over an algebraically closed field $K$ of characteristic zero. A subalgebra $L \subseteq W_n(\mathbb{K})$ is called polynomial if it is a submodule of the $\mathbb{K}[X]$-mo...
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| Дата: | 2011 |
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| Автори: | , , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2011
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2755 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | Let $W_n(\mathbb{K})$ be the Lie algebra of derivations of the polynomial algebra $\mathbb{K}[X] := \mathbb{K}[x_1,... ,x_n]$ over an algebraically closed field $K$ of characteristic zero.
A subalgebra $L \subseteq W_n(\mathbb{K})$ is called polynomial if it is a submodule of the $\mathbb{K}[X]$-module $W_n(\mathbb{K})$.
We prove that the centralizer of every nonzero element in $L$ is abelian provided that $L$ is of rank one.
This fact allows to classify finite-dimensional subalgebras in polynomial Lie algebras of rank one. |
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