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Or equivalently, why is jacobi identity equivalent to integrability of system? How do I understand it intuitively? Thanks.

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    $\begingroup$ Could you say more explicitly what you mean by the Jacobi identity and the holonomy of system? $\endgroup$
    – Deane Yang
    Commented Mar 20, 2019 at 3:37
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    $\begingroup$ Once we make sense of the intended question, it's answered by Chapter II.3 of Baez-Muniain's book "Gauge fields, knots, and gravity". $\endgroup$
    – Chris Gerig
    Commented Mar 20, 2019 at 3:41
  • $\begingroup$ not an answer, but reference to math.stackexchange.com/questions/113766/… $\endgroup$
    – N.Li
    Commented Dec 24, 2019 at 3:09

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