Displaying similar documents to “Homology and modular classes of Lie algebroids”

Modular vector fields and Batalin-Vilkovisky algebras

Yvette Kosmann-Schwarzbach (2000)

Banach Center Publications

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We show that a modular class arises from the existence of two generating operators for a Batalin-Vilkovisky algebra. In particular, for every triangular Lie bialgebroid (A,P) such that its top exterior power is a trivial line bundle, there is a section of the vector bundle A whose d P -cohomology class is well-defined. We give simple proofs of its properties. The modular class of an orientable Poisson manifold is an example. We analyse the relationships between generating operators of the...

Algebroid nature of the characteristic classes of flat bundles

Jan Kubarski (1998)

Banach Center Publications

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The following two homotopic notions are important in many domains of differential geometry: - homotopic homomorphisms between principal bundles (and between other objects), - homotopic subbundles. They play a role, for example, in many fundamental problems of characteristic classes. It turns out that both these notions can be - in a natural way - expressed in the language of Lie algebroids. Moreover, the characteristic homomorphisms of principal bundles (the Chern-Weil homomorphism [K4],...

The BV-algebra of a Jacobi manifold

Izu Vaisman (2000)

Annales Polonici Mathematici

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We show that the Gerstenhaber algebra of the 1-jet Lie algebroid of a Jacobi manifold has a canonical exact generator, and discuss duality between its homology and the Lie algebroid cohomology. We also give new examples of Lie bialgebroids over Poisson manifolds.

Tangent lifts of higher order of multiplicative Dirac structures

P. M. Kouotchop Wamba, A. Ntyam (2013)

Archivum Mathematicum

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The tangent lifts of higher order of Dirac structures and some properties have been defined in [9] and studied in [11]. By the same way, the tangent lifts of higher order of Poisson structures have been studied in [10] and some applications are given. In particular, the authors have studied the nature of the Lie algebroids and singular foliations induced by these lifting. In this paper, we study the tangent lifts of higher order of multiplicative Poisson structures, multiplicative Dirac...

The Weil algebra and the Van Est isomorphism

Camilo Arias Abad, Marius Crainic (2011)

Annales de l’institut Fourier

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This paper belongs to a series of papers devoted to the study of the cohomology of classifying spaces. Generalizing the Weil algebra of a Lie algebra and Kalkman’s BRST model, here we introduce the Weil algebra W ( A ) associated to any Lie algebroid A . We then show that this Weil algebra is related to the Bott-Shulman complex (computing the cohomology of the classifying space) via a Van Est map and we prove a Van Est isomorphism theorem. As application, we generalize and find a simpler more...