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Integrable lifts for transitive Lie algebroids. (arXiv:1707.04855v3 [math.DG] UPDATED)
来源于:arXiv
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. 查看全文>>