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What is an appropriate version of the following fact in terms of Hopf algebras and quantum groups:

"For every connected Lie group $G$ the second fundamental group $\pi_2(G)$ is trivial?"

Is there any research in this direction?

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    $\begingroup$ Well, it's true for non-connected Lie groups too. Also, you want "finite-dimensional" in there. The loop group of a Lie group has a nonzero $\pi_2$. $\endgroup$
    – David Roberts
    Mar 16, 2020 at 20:23
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    $\begingroup$ It should be kept in mind that maybe there is no analogue, in the sense that for non-classical quantum groups such a phenomenon does not occur. $\endgroup$
    – Yemon Choi
    Mar 16, 2020 at 20:30
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    $\begingroup$ quantum groups are more degenerations of (universal enveloping algebras of) Lie algebras than they are of Lie groups per se; is there a purely algebraic reformulation of the vanishing of $\pi_2$ statement? $\endgroup$ Mar 16, 2020 at 23:04

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