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.

Full Text

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},
}