Centralizers of elements in Lie algebras of derivations of fields

Authors

  • S. V. Lysenko Kyiv National Taras Shevchenko University, Mechanics and Mathematics faculty
  • A. P. Petravchuk Kyiv National Taras Shevchenko University, Mechanics and Mathematics faculty
  • V. V. Stepukh Kyiv National Taras Shevchenko University, Mechanics and Mathematics faculty

Abstract

Let $K$ be an algebraically closed field of characteristic zero and $R$ an algebraic extension of the field of rational functions $K(x_1,.,x_n)$ in $n$ variables. We study centralizers of elements in the Lie algebra $Der_{K}R$ of all $K$-derivations of the field $R.$
If $F$ is the field of constants of a derivation $D\in Der _{K}R$ on $R$ and $tr.deg_{K}F\leq2$ then a characterization of the centralizer $C_{Der_{K}(R)}(D)$ is given depedent on $tr.deg_{K}F.$

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Published

2015-05-05

Issue

Vol. 12 No. 1 (2015): Spectral theory of operators and of collections of operators

Section

Research papers

How to Cite

Centralizers of elements in Lie algebras of derivations of fields. (2015). Transactions of Institute of Mathematics, the NAS of Ukraine, 12(1), 141-153. https://trim.imath.kiev.ua/index.php/trim/article/view/10