Open Access

On finite dimensional Lie algebras of planar vector fields with rational coefficients

Abstract

The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as subalgebras of this algebra.

Key words: Lie algebra, vector field, derivation, finite dimensional subalgebra.

Article Information

 Title On finite dimensional Lie algebras of planar vector fields with rational coefficients Source Methods Funct. Anal. Topology, Vol. 19 (2013), no. 4, 376-388 MathSciNet MR3156302 zbMATH 1313.81010 Milestones Received 29/04/2013 Copyright The Author(s) 2013 (CC BY-SA)

Authors Information

Ie. Makedonskyi
Kyiv Taras Shevchenko University, 64 Volodymyrs'ka, Kyiv, 01601, Ukraine

A. Petravchuk
Kyiv Taras Shevchenko University, 64 Volodymyrs'ka, Kyiv, 01601, Ukraine

Citation Example

Ie. Makedonskyi and A. Petravchuk, On finite dimensional Lie algebras of planar vector fields with rational coefficients, Methods Funct. Anal. Topology 19 (2013), no. 4, 376-388.

BibTex

@article {MFAT695,
AUTHOR = {Makedonskyi, Ie. and Petravchuk, A.},
TITLE = {On finite dimensional Lie algebras of planar vector fields with rational coefficients},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {19},
YEAR = {2013},
NUMBER = {4},
PAGES = {376-388},
ISSN = {1029-3531},
MRNUMBER = {MR3156302},
ZBLNUMBER = {1313.81010},
URL = {http://mfat.imath.kiev.ua/article/?id=695},
}