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.In the diagram 12 l-\ I it is evident that the corresponding fundamental roots pi, pz, . . . , pi-i all have the same length, but pi ... For the same reason there is only one fundamental root system of type Gz and one of type Ft, since the diagrams areanbsp;...
|Title||:||Simple Groups of Lie Type|
|Author||:||Roger W. Carter|
|Publisher||:||John Wiley & Sons - 1989-01-18|