%0 Journal Article
%T A remark about the Lie algebra of infinitesimal conformal transformations of the Euclidian space
%A F. Boniver
%A P. B. A. Lecomte
%J Mathematics
%D 1999
%I arXiv
%X Infinitesimal conformal transformations of $R^n$ are always polynomial and finitely generated when $n>2$. Here we prove that the Lie algebra of infinitesimal conformal polynomial transformations over $R^n$, $n>1$, is maximal in the Lie algebra of polynomial vector fields. When $n$ is greater than 2 and $p,q$ are such that $p+q=n$, this implies the maximality of an embedding of $so(p+1,q+1,R)$ into polynomial vector fields that was revisited in recent works about equivariant quantizations. It also refines a similar but weaker theorem by V. I. Ogievetsky.
%U http://arxiv.org/abs/math/9901034v1