ANALYSIS and GEOMETRY in FOLIATED MANIFOLDS, World Scientific, Singapure 1995, 137-151; Proceedings of the VII International Collóquium on Differential Geometry, Santiago de Compostela, Spain 26-30 July, 1994.
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We look at the classical theorem dealing with invariant cohomology from the viewpoint of the theory of Lie algebroids. Its generalization concerning an action of a compact Lie group on a regular Lie algebroid is obtained.
Main Theorem: Let T : G × A ® A be an action of a Lie group G on a regular Lie algebroid A, extending to a homomorphism of Lie algebroids T : TG × A ® A that is, to a homomorphism of Lie algebroids T such that T|G × A = T. If G is compact, then the inclusion i : WA,I(M) ® WA(M) induces a monomorphism on cohomology. If, additionally, G is connected, then the inclusion induces an isomorphism.
Some applications to tangential cohomology and actions on vector bundles are given.