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Lie's Third Theorem states that any real (finite-dimensional) Lie algebra has associated a Lie group. Moreover, this Lie group is a matrix group.

I'm interested to Lie algebras over $\mathbb{C}$ and finite exitensions of $\Bbb Q_p$. Does there exist an analogue of Lie's Third Theorem to such algebras? If so, do you have any reference which I can check?

Thank you.

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    $\begingroup$ It seems to have a positive answer, see proposition 17.3 in Schneider's book $p$-adic Lie Groups. $\endgroup$ – Watson May 27 '18 at 19:51

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