Lie groups and Lie algebras: Root systems

We introduce the notion of a root system, which abstracts the properties common to root diagrams of compact semisimple Lie groups. We prove that root diagrams have all the required properties.

[@Gloveless_Surgery]

I just cannot thank you enough for the content you provide here on CZcams, it is and has been immensely helpful in my studies!

[@terencecoelho5940]

Had this funny realization the other day that the "finiteness" of a finite (reduced or not-necessarily-reduced) root system can be deduced from the other axioms, and therefore need not be listed as an axiom. I've scoured all over for a single text that acknowledges this or omits "finiteness" from the list of axioms, and this is the only place I've found it omitted. Was this intentional?

[@sebastiandierks7919]

I guess in the axioms 2, 3 and 4, you used both l_alpha and lambda_alpha for the line through alpha. In earlier videos of the playlist, you used lambda already for (highest) weights, so I guess calling it l_alpha is a bit clearer.