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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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Center of the algebraic group $G_{\mathbb{R}}$ for a centerless $G$

The short answer is that the center Z(G) of a semisimple algebraic group is a well-defined (finite) algebraic subgroup which commutes with extension of the base field, so if it's trivial over $\mathbb …
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