Chevalley Group

The Chevalley groups are a family of finite simple groups constructed uniformly from the root systems of complex simple Lie algebras. Introduced by Claude Chevalley in the 1950s, they provide a single recipe that produces finite analogues of all classical simple Lie groups — as well as exceptional groups that have no classical counterpart — over arbitrary fields. The construction begins with a simple Lie algebra over the complex numbers, selects a Chevalley basis (a basis with integer structure constants), and then evaluates the associated matrix group over a finite field. The resulting groups are almost always simple, and they account for many of the infinite families in the classification of finite simple groups.