Abstract
A simple construction associates to any linear mapping a short exact sequence of graded Lie algebras. The sequence associated to the de Rham differential of an arbitrary smooth manifold is never split. Combined with a sort of “algebraic” Chern-Weil homomorphism adapted from [1] to the graded case, this leads to a family of cohomology classes of the Nijenhuis-Richardson algebra of the space of functions of the manifold. Some of these “characteristic classes” of degree 2 are computed. They are the classes constructed by hand in [2] and used in the theory of star-products.
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Communicated by P. Michor
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Lecomte, P.B.A. On some sequence of graded Lie algebras associated to manifolds. Ann Glob Anal Geom 12, 183–192 (1994). https://doi.org/10.1007/BF02108296
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DOI: https://doi.org/10.1007/BF02108296