Finitedimensional subalgebras in polynomial Lie algebras of rank one
Abstract
Let W_n(K) be the Lie algebra of derivations of the polynomial algebra K[X]:=K[x_1,...,x_n] over an algebraically closed field K of characteristic zero. A subalgebra L of W_n(K) is called polynomial if it is a submodule of the K[X]module W_n(K). We prove that the centralizer of every nonzero element in L is abelian provided L has rank one. This allows to classify finitedimensional subalgebras in polynomial Lie algebras of rank one.
 Publication:

arXiv eprints
 Pub Date:
 May 2010
 arXiv:
 arXiv:1005.1415
 Bibcode:
 2010arXiv1005.1415A
 Keywords:

 Mathematics  Rings and Algebras;
 17B66;
 16W25;
 17A36
 EPrint:
 5 pages