Centralizers of Jacobian derivations

• Date: 2023
• Main Authors: Efimov, D. I., Petravchuk, A. P., Sydorov, M. S.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2023
• Subjects: Lie algebra; Jacobian derivation; differential equation; centralizer; integrable system; Primary 17B66; Secondary 17B80
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2186
• Journal Title: Algebra and Discrete Mathematics

Let \(\mathbb K\) be an algebraically closed field of characteristic zero, \(\mathbb K[x, y]\) the polynomial ring in variables \(x\), \(y\) and let \(W_2(\mathbb K)\) be the Lie algebra of all \(\mathbb K\)-derivations on \(\mathbb K[x, y]\). A derivation \(D \in W_2(\mathbb K)\) is called a Jacobi...