Skip to main content



Simple Groups of Lie Type

Roger W. Carter

ISBN: 978-0-471-50683-6 January 1989 364 Pages


Now available in paperback--the standard introduction to the theory of simple groups of Lie type. In 1955, Chevalley showed how to construct analogues of the complex simple Lie groups over arbitrary fields. The present work presents the basic results in the structure theory of Chevalley groups and their twisted analogues. Carter looks at groups of automorphisms of Lie algebras, makes good use of Weyl group (also discussing Lie groups over finite fields), and develops the theory of Chevalley and Steinberg groups in the general context of groups with a (B,N)-pair. This new edition contains a corrected proof of the simplicity of twisted groups, a completed list of sporadic simple groups in the final chapter and a few smaller amendments; otherwise, this work remains the classic piece of exposition it was when it first appeared in 1971.
Partial table of contents:

The Classical Simple Groups.

Weyl Groups.

Simple Lie Algebras.

The Chevalley Groups.

Unipotent Subgroups.

The Diagonal and Monomial Subgroups.

The Bruhat Decomposition.

Polynomial Invariants of the Weyl Group.

The Exponents of the Weyl Group.

Further Properties of the Chevalley Groups.

Generators, Relations and Automorphisms in Chevalley Groups.

The Twisted Simple Groups.

Further Properties of the Twisted Groups.

Associated Geometrical Structures.

Sporadic Simple Groups.


Index of Notation.