A remark about the Lie algebra of infinitesimal conformal transformations of the Euclidian space
نویسنده
چکیده
Infinitesimal conformal transformations of IRn are always polynomial and finitely generated when n > 2. Here we prove that the Lie algebra of infinitesimal conformal polynomial transformations over IRn, 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, IR) 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. AMS classification numbers : 17B66, 53A30
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