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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

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$G_2$ and Geometry

I promised Sean a detailed answer, so here it is. As José has already mentioned, it is only $G_2$ (of the five exceptional Lie groups) which can arise as the holonomy group of a Riemannian manifold. …
Spiro Karigiannis's user avatar