On the integrability of transitive Lie algebroids

Abstract: We discuss an approach to the integration problem for general transitive Lie algebroids using two basic ingredients: the Čech cohomology and the generalization of smooth manifolds that was proposed by Raymond Barre under the name of Q-manifolds. To this end we study the notion of Q-principal bundle, i.e., a natural version of principal fibre bundles in the theory of Q-manifolds. We then prove that every transitive Lie algebroid arises from the Atiyah sequence of a Q-principal bundle and we give the interpretation of that result in terms of groupoids. The presentation is based on joint work with Fernand Pelletier.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

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Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

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