Abstract
Letkbe an integral domain, letF= (F1X, Y),…,Fn(X, Y)),X= (X1,…,Xn),Y= (Y1,…,Yn), be ann-dimensional formal group overk, and letL(F) be the Lie algebra of allF-invariantk-derivations of the ring of formal power seriesk[X] (cf. § 2). If A is a (commutative)k-algebra and Derk(A) denotes the Lie algebra of allk-derivationsd:A→A, then by an action ofL(F) onAwe mean a morphism of Lie algebrasφ:L(F) → Derk(A) such thatφ(dp) = φ(d)p, provided char (k) =p> 0. An action of the formal groupFonAis a morphism ofk-algebrasD:A-→A[X] such thatD(a)≡a mod (X) fora ∊ A, andFA∘D=DY∘D, whereFA:A[X] →A[X, Y],DF:A[X] →A[X, Y] are morphisms ofk-algebras given byFA(g(X))=g(F), DY(ΣaaaXa) =ΣaD(aa)Y;for a motivation of this notion, see [15]. LetD:A→A[X] be such an action.
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