Department of Applied Mathematics, University of Twente
Abstract
We study finite-dimensional Lie algebras of polynomial vector fields in n variables that contain the vector fields ∂/∂xi(i=1,…,n) and x1∂/∂x1+⋯+xn∂/∂xn. We derive some general results on the structure of such Lie algebras, and provide the complete classification in the cases n=2 and n=3. Finally we describe a certain construction in high dimensions