A remark about the Lie algebra of infinitesimal conformal transformations of the Euclidian space

1999/01/08 by F. Boniver, Boniver, F., P. B. A. Lecomte +2 · 1 citation
Mathematics · Physics and Astronomy · #17B66 #53A30 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.DG #math.RT #msc:17B66 #msc:53A30

paper · pdf · doi:10.48550/arxiv.math/9901034

LaTeX source, 4 pages

arxiv created 1999/01/08 · openalex publication_date 1999/01/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Infinitesimal conformal transformations of Rⁿ are always polynomial and finitely generated when n>2. Here we prove that the Lie algebra of infinitesimal conformal polynomial transformations over Rⁿ, 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.

Citations

• Conformally equivariant quantization

Cited by

• Infinitesimal Conformal Rigidity on Damek-Ricci Spaces

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