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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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Representation of Lie algebra $\operatorname{SE}(2)$

The representation $R$ can be seen as a map: $$R:\operatorname{SE} (2)\to\operatorname{Diff}(\mathbb R^2) $$ and the derivations above correctly allows to compute the corresponding infinitesimal actio …
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