01299nas a2200145   4500008004100000245005100041210005100092520086700143653001001010653001001020653004001030100002201070700002001092856004101112       2017                        eng d00aIntegrable lifts for transitive Lie algebroids0 aIntegrable lifts for transitive Lie algebroids3 a<p><span style="font-family: -webkit-standard; font-size: medium;">Inspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove that the Weinstein groupoid of a non-integrable transitive and abelian Lie algebroid, is the quotient of a finite dimensional Lie groupoid. Two constructions as such are given: First, explaining the counterexample to integrability given by Almeida and Molino, we see that it can be generalized to the construction of an "Almeida-Molino" integrable lift when the base manifold is simply connected. On the other hand, we notice that the classical de Rham isomorphism provides a universal integrable algebroid. Using it we construct a "de Rham" integrable lift for any given transitive Abelian Lie algebroid.</span></p>10a14F4010a58H0510aMathematics - Differential Geometry1 aAndroulidakis, I.1 aAntonini, Paolo  uhttps://arxiv.org/pdf/1707.04855.pdf