Abstract
Vector fields on smooth manifolds may be regarded as derivations of the algebra of smooth functions, as infinitesimal generators of flows, or as sections of the tangent bundle. The last point of view leads to a formula for the bracket which is not used very often and in terms of which such a basic matter as provingth e Jacobi identity seems difficult. We present a conceptually simple proof of the Jacobi identity in terms of this formulation.
Mathematics Subject Classification (2010). Primary 58A99; Secondary 18D05.
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Mackenzie, K. (2013). Proving the Jacobi Identity the Hard Way. In: Kielanowski, P., Ali, S., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0448-6_32
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DOI: https://doi.org/10.1007/978-3-0348-0448-6_32
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