Graded vector fields and involutive distributions on graded manifolds

Abstract

Abstract Suppose that ℳ = (M, 𝒜M) is a graded manifold and consider a direct subsheaf 𝒟 of Der 𝒜ℳ and a graded vector field Γ on ℳ, both satisfying certain conditions. We attach to 𝒟 a distribution 𝒟 + [Γ, 𝒟] and characterize its maximal rank with respect to dim ℳ. 𝒟 is used to characterize the local expression of Γ.