I gather (via this nice MO comment) that

The functor that takes linear algebraic groups $G$ to their $\mathbb{R}$-points $G(\mathbb{R})$ constitutes an equivalence of categories between compact Lie groups and $\mathbb{R}$-aniosotropic reductive algebraic groups over $\mathbb{R}$ all whose connected components have $\mathbb{R}$-points.

For $G$ as in this equivalence, then then complex Lie group $G(\mathbb{C})$ is the complexification of $G(\mathbb{R})$.

I have a gap in my education here and would like to fill it. What’s a good source that discusses this statement a bit more? And which one of Chevalley’s articles is this result originally due?

]]>