This book is a revised and enlarged edition of "Linear Algebraic Groups," published by W.A. Benjamin in 1969. The text of the first edition has been corrected and revised. Accordingly, this book presents foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. After establishing these basic topics, the text then turns to solvable groups, general properties of linear algebraic groups and Chevally's structure theory of reductive groups over algebraically closed groundfields. The remainder of the book is devoted to rationality questions over non-algebraically closed fields. This second edition has been expanded to include material on central isogenies and the structure of the group of rational points of an isotropic reductive group. The main prerequisite is some familiarity with algebraic geometry. The main notions and results needed are summarized in a chapter with references and brief proofs.
|Background Material from Algebraic Geometry|
|General Notions Associated with Algebraic Groups|
|Borel Subgroups; Reductive Groups|
|Index of Definition|
|Index of Notation|
|Table of Contents provided by Publisher. All Rights Reserved.|
Series: Graduate Texts in Mathematics
Number Of Pages: 290
Published: April 1991
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.1 x 16.4 x 2.3
Weight (kg): 0.62
Edition Number: 2
Edition Type: Revised