Lie Algebroids Associated with Deformed Schouten Bracket of 2-Vector Fields.

Given a 2-vector field and a closed 1-form on a manifold, we consider the set of cotangent vectors which annihilate the deformed Schouten bracket of the 2-vector field by the closed 1-form. We show that if the space of cotangent vectors forms a vector bundle, it carries a structure of a Lie algebroid. We treat this theorem in the category of Lie algebroids. As a special case, this result contains the well-known fact that the 1-jet bundle of functions of a contact manifold has a Lie algebroid structure. [ABSTRACT FROM AUTHOR]