On noncommutative bases of the free module W_n(\mathbb K)

2011/05/24 by Makedonskyi, Ievgen
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1105.4748

Abstract

Let \mathbbK be an algebraically closed field of characteristic zero and R=\mathbbK[x₁,x₂,...x_n] the polynomial ring in n variables over \mathbb K. We study bases of the free R-module W_n(\mathbbK) of all \mathbbK-derivations of the ring R, such that their linear span over \mathbb K is a subalgebra of the Lie algebra W_n(\mathbbK). We proved that for any Lie algebra L of dimension n over \mathbbK there exists a subalgebra L of W_n(\mathbbK) which is isomorphic to L and such that every \mathbbK-basis of L is an R-basis of the R-module W_n(\mathbbK).

Related

• The freeness property for locally nilpotent derivations of k[x,y,z]
• Module structure of the Lie algebra W_n(K) over sl_n(K)
• Symmetric polynomials in the free metabelian Lie algebras
• On the annihilators of rational functions in the Lie algebra of derivations of k[x, y]
• Classical invariant theory for free metabelian Lie algebras