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

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dc.creatorBoniver, F.
dc.creatorLecomte, P. B. A.
dc.date1999-01-08
dc.date.accessioned2026-07-07T05:27:30Z
dc.date.available2026-07-07T05:27:30Z
dc.descriptionInfinitesimal 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.
dc.descriptionLaTeX source, 4 pages
dc.identifierhttps://arxiv.org/abs/math/9901034
dc.identifierhttp://arxiv.org/abs/math/9901034
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77940
dc.subjectDifferential Geometry
dc.subjectRepresentation Theory
dc.subject17B66; 53A30
dc.titleA remark about the Lie algebra of infinitesimal conformal transformations of the Euclidian space
dc.typetext

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