Lie algebras of derivations with large abelian ideals

• Date: 2019
• Main Authors: Klymenko, I. S., Lysenko, S. V., Petravchuk, Anatoliy
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2019
• Subjects: Lie algebra; vector field; polynomial ring; abelian ideal; derivation; 17B66; 17B05; 13N15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/273
• Journal Title: Algebra and Discrete Mathematics

Let \(\mathbb K\) be a field of characteristic zero, \(A=\mathbb{K}[x_{1},\ldots ,x_{n}]\) the polynomial ring and \(R=\mathbb{K}(x_{1},\dots,x_{n})\) the field of rational functions. The Lie algebra \({\widetilde W}_{n}(\mathbb{K}):=\operatorname{Der}_{\mathbb{K}}R\) of all \(\mathbb{K}\)-derivatio...