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arXiv · 1005.1415

Finite-dimensional subalgebras in polynomial Lie algebras of rank one

I. V. Arzhantsev·E. A. Makedonskii·A. P. Petravchuk
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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 finite-dimensional subalgebras in polynomial Lie algebras of rank one.

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I. V. Arzhantsev, E. A. Makedonskii, A. P. Petravchuk. 2010-05-09. Finite-dimensional subalgebras in polynomial Lie algebras of rank one. https://arxiv.org/abs/1005.1415

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