Sur les algèbres de lie d'un système de champs de vecteurs permutables

Abstract

Let be M a C^ꝏ — differentiable manifold and S a system of q C^ꝏ — vector fields which commute mutually. This system defines a generalized foliation \(\mathcal{F}\) on M.  The Lie algebra A_S of vector fields in M which commute with S is both a module
over the ring of C^ꝏ — functions that are constant on the leaves of \(\mathcal{F}\) and a sub-Lie algebra of the foliation preserving vector fields.  We determine all derivations of the Lie algebra A_S.