Chevalley group

Summary

A Chevalley group is a group of automorphisms of a simple Lie algebra rebuilt over an arbitrary field. The rebuilding uses the integral structure given by a Chevalley basis. Claude Chevalley introduced this construction in 1955. It gives, in a uniform way, a simple group for each simple complex Lie algebra and each field, apart from a few small exceptions. Over finite fields these groups give most of the families of finite simple groups of Lie type, including new families of exceptional type.