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Daniel Beltita (Institute of Mathematics "Simion Stoilow" of the Romanian Academy of Sciences)
2025-02-19 12:30 - 13:30 UTC | https://researchseminars.org/talk/PHK-cohomology-seminar/120/
Title: On the integrability of transitive Lie algebroids (https://researchseminars.org/talk/PHK-cohomology-seminar/120/)
by Daniel Beltita (Institute of Mathematics "Simion Stoilow" of the Romanian Academy of Sciences) as part of Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

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.
