Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-27T02:50:31.000Z Has data issue: false hasContentIssue false
  • English
  • Français

A REMARK ABOUT THE LIE ALGEBRA OF INFINITESIMAL CONFORMAL TRANSFORMATIONS OF THE EUCLIDEAN SPACE

Published online by Cambridge University Press:  01 May 2000

F. BONIVER  and
P. B. A. LECOMTE
F. BONIVER
Affiliation:
Institut de Mathématique, B37, Grande Traverse, 12, B-4000 Sart Tilman (Liège), Belgium
P. B. A. LECOMTE
Affiliation:
Institut de Mathématique, B37, Grande Traverse, 12, B-4000 Sart Tilman (Liège), Belgium
Get access

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 > 2, 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.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 3 , May 2000 , pp. 263 - 266
Copyright
© The London Mathematical Society 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)