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

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 an...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2000-05, Vol.32 (3), p.263-266
Main Authors: BONIVER, F., LECOMTE, P. B. A.
Format: Article
Language:English
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Summary: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.
ISSN:0024-6093
1469-2120
DOI:10.1112/S0024609300006986