The Lie Algebra of Smooth Sections of aT-bundle

In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of aT-bundle which is by definition a canonical generalization of the concept of a tangent bundle. We define a Lie bracket multiplication on this set so that it becomes a Lie algebra. In the particular case of tangent bundles this Lie algebra coincides with the Lie algebra of vector fields.