Finite-dimensional subalgebras in polynomial Lie algebras of rank one

Details Finite-dimensional subalgebras in polynomial Lie algebras of rank one Finite-dimensional subalgebras in polynomial Lie algebras of rank one

2010-05-09

arxiv.org/abs/1005.1415v1

Ukrainian Math. Journal 63 (2011), no. 5, 827 - 832

Mathematics

Rings and Algebras

5 pages

Scientific paper

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 finite-dimensional subalgebras in polynomial Lie algebras of rank one.

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