alexa The m-Derivations of Distribution LieAlgebras

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The m-Derivations of Distribution LieAlgebras

 Let M be a N-dimensional smooth differentiable manifold. Here, we are going to analyze (m>1)-derivations of Lie algebras relative to an involutive distribution on subrings of real smooth functions on M. First, we prove that any (m>1)-derivations of a distribution Ω on the ring of real functions on M as well as those of the normalizer of Ω are Lie derivatives with respect to one and only one element of this normalizer, if Ω doesn’t vanish everywhere. Next, suppose that N = n + q such that n>0, and let S be a system of q mutually commuting vector fields. 

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