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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
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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

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