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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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Harmonicity on semisimple groups
I asked this on Math.SE and got no answer, so I'll try my luck here.
Let $G$ be a semisimple real Lie group, $U(\mathfrak{g})$ its universal enveloping algebra, let $\Omega$ be the Casimir element in …