# What are the implications of integrating the Poisson bracket?

Reading Ref. 1 I admit I am a little lost in some places. I was hoping that someone in this area could explain the basic premise of integrating the Lie bracket and further is it connected to nlab's Quantomorphism group? If this is so, can we 'derive' a quantum system by Lie integration of a Poisson algebra of observables?

References:

1. M. Crainic, R. L. Fernandes, "Integrability of Poisson Brackets", J. Differential Geometry, 66, (2004), 7. (PDF)
2. http://ncatlab.org/nlab/show/quantomorphism+group
• Just a comment to the 'close' flag, why do you think this is off topic? – AngusTheMan Nov 20 '15 at 14:47
• Just a guess, but this seems to be a "pure mathematics" question rather than a "physics" one. – Alex Nelson Jun 15 '17 at 15:42
• At this level of formal exactitude, I should agree with @Alex_Nelson that this is worse than pure math. In physics, of course, "as every child knows" at the practical level suited for solving concrete problems, the group generated by the PBs is just $SU(\infty)$, cf this mini review. – Cosmas Zachos Jul 8 '18 at 19:35