Linear Algebraic Groups

  • Armand┬áBorel

Part of the Graduate Texts in Mathematics book series (GTM, volume 126)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Armand Borel
    Pages 89-110
  3. Armand Borel
    Pages 111-146
  4. Armand Borel
    Pages 147-202
  5. Armand Borel
    Pages 203-279
  6. Back Matter
    Pages 280-290

About this book


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.


Lie algebra algebra algebraic group commutative algebra linear algebra

Authors and affiliations

  • Armand┬áBorel
    • 1
  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York Inc. 1991
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6954-0
  • Online ISBN 978-1-4612-0941-6
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site
Industry Sectors
Energy, Utilities & Environment