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A property of the ideals of finite codimension of the Lie algebras of vector fields. (Une propriété des idéaux de codimension finie des algèbres de Lie de champs de vecteurs.) (French) Zbl 1079.17009

The authors analize ideals in the Lie algebra of smooth vector fields which have finite codimension. It is shown that a large class of subalgebras have the property of containing, in some ideal of finite codimension, the ideal of germs which are flat at the origin. This is further employed to reduce the action of the group of germs which preserve diffeomorphisms to the action of the group of infinite jets.

MSC:

17B66 Lie algebras of vector fields and related (super) algebras
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