In 1955, Chevalley proved the then surprising theorem that split semi-simple algebraic groups could be associated to every root system and defined over any ground field.The basic point in the construction was that complex semi-simple Lie algebras could be assigned an essentially unique Z -structure, in which the formulas for structure constants were particularly simple.His proof, which is that usually followed in the literature, does not appear transparent.In this paper, I'll show how an idea implicitly due to Jacques Tits leads to a more natural derivation.It remains valid for Kac-Moody algebras.
B. Casselman (Thu,) studied this question.