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Abstract Let X = \X₀, , Xₘ\ X = X 0, …, X m be a family of smooth vector fields on an open set RN Ω ⊆ R N. Motivated by applications to the PDE theory of Hörmander operators, for a suitable class of open sets Ω, we find necessary and sufficient conditions on X for the existence of a Lie group (, *) (Ω, ∗) such that the operator L= ₈ = ₁ᵐXᵢ²+X₀ L = ∑ i = 1 m X i 2 + X 0 is left-invariant with respect to the operation * ∗. Our approach is constructive, as the group law is constructed by means of the solution of a suitable ODE naturally associated to vector fields in X. We provide an application to a partial differential operator appearing in the Finance.
Biagi et al. (Wed,) studied this question.
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