Soit V une variété complexe et soit I le champ de tenseurs de type (1,1) de V définissant la structure complexe de V. Un champ de vecteurs ξ sur V sera dit conforme si I [ξ, η]= [ξ, Iη] pour tout champ de vecteurs η sur V. On désignera par α l’ensemble de tous les champs de vecteurs comformes sur V. α est une sous-algèbre de Lie de l’algèbre de Lie de tous les champs de vecteurs sur V. Si V est compacte, α est de dimension finie et s’identifie avec l’algèbre de Lie du groupe de Lie A(V) d’homéomorphismes analytiques de V [2] De plus, si ξ, η ∈ α, on a On peut donc définir une structure d’algèbre de Lie complexe de α en posant pour tout ξ ∈ α.

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This note is a sequel to the previous one [l ], and is devoted to some applications of the results of the latter to adele groups. The results are valid for linear algebraic groups defined over number fields, but this case is easily reduced to that of groups defined over 0 [3, Chapter I], to which we shall limit ourselves for simplicity. The notation of [l] is freely used. For the unexplained notions concerning adeles, see [2; 3].

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