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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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Fourier transform of a matrix represented compact lie group

In physics, I come across this kind of integration (in the nonlinear sigma model): \begin{equation} S[g] = \frac{1}{\lambda} \int d^dr\ \text{tr}[\triangledown g\triangledown g^{-1}] \end{equation} wh …