The Peter-Weyl Theorem

Intuitive

Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.

Concrete

“A real, connected, semi-simple Lie group G is compact if and only if its corresponding real Lie algebra is compact.” https://campusvirtual.univalle.edu.co/moodle/pluginfile.php/66702/mod_resource/content/0/Lie-Stetz-U-Oregon.pdf

Abstract

The motto in this section is: the higher the level of abstraction, the better.

Why is it interesting?