The Lie Algebra of Smooth Sections of aT-bundle

In this article, we generalize the concept of the lie algebra of vector fieldsto the set of smooth sections of at-bundle which is by definition a canonicalgeneralization of the concept of a tangent bundle. we define a lie bracketmultiplication on this set so that it becomes a lie algebra. in the particular case oftangent bundles this lie algebra coincides with the lie algebra of vector fields.