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If A is an integrable and transitive Lie Algebroid, and G is a corresponding Lie groupoid, then: is G necessarily transitive too? I guess it is not generally true, but I wonder under which conditions this is true?

Let me know if someone has the answer/relevant references ;)

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If the base manifold M is connected, and A is such a Lie algebroid then the only orbit of A is M itself. It turns out that one can always find a Lie groupoid (called the Weinstein groupoid by Crainic & Fernandes) integrating A and which has the same orbits as A, i.e. which is transitive too.

Ref.: Lectures of Integrability of Lie Brackets, Crainic & Fernandes (2006)

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