
Journal of Lie Theory 25 (2015), No. 2, 431441 Copyright Heldermann Verlag 2015 On Chevalley's Formula for Structure Constants Bill Casselman Dept. of Mathematics, University of British Columbia, Vancouver V6T 1Z2, Canada cass@math.ubc.ca In 1955, Chevalley proved the then surprising theorem that split semisimple algebraic groups could be associated to every root system and defined over any ground field. The basic point in the construction was that complex semisimple Lie algebras could be assigned an essentially unique Zstructure, 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 KacMoody algebras. Keywords: Semisimple Lie algebras, structure constants, Chevalley groups. MSC: 17B45 [ Fulltextpdf (152 KB)] for subscribers only. 