Displaying similar documents to “Nondegenerate cohomology pairing for transitive Lie algebroids, characterization”

Leibniz cohomology for differentiable manifolds

Jerry M. Lodder (1998)

Annales de l'institut Fourier

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We propose a definition of Leibniz cohomology, H L * , for differentiable manifolds. Then H L * becomes a non-commutative version of Gelfand-Fuks cohomology. The calculations of H L * ( R n ; R ) reduce to those of formal vector fields, and can be identified with certain invariants of foliations.

The local integration of Leibniz algebras

Simon Covez (2013)

Annales de l’institut Fourier

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This article gives a local answer to the coquecigrue problem for Leibniz algebras, that is, the problem of finding a generalization of the (Lie) group structure such that Leibniz algebras are the corresponding tangent algebra structure. Using links between Leibniz algebra cohomology and Lie rack cohomology, we generalize the integration of a Lie algebra into a Lie group by proving that every Leibniz algebra is isomorphic to the tangent Leibniz algebra of a local Lie rack. This article...

The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids

Jan Kubarski (2006)

Czechoslovak Mathematical Journal

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This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either or s l ( 2 , ) or so ( 3 ) are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to n + 1 , where n is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For -Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf...