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Linear Algebraic Groups

  • T. A. Springer

Part of the Modern Birkhäuser CIassics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. T. A. Springer
    Pages 1-20
  3. T. A. Springer
    Pages 21-41
  4. T. A. Springer
    Pages 42-56
  5. T. A. Springer
    Pages 57-77
  6. T. A. Springer
    Pages 114-131
  7. T. A. Springer
    Pages 132-153
  8. T. A. Springer
    Pages 154-174
  9. T. A. Springer
    Pages 175-184
  10. T. A. Springer
    Pages 185-207
  11. T. A. Springer
    Pages 208-222
  12. T. A. Springer
    Pages 223-236
  13. T. A. Springer
    Pages 238-251
  14. T. A. Springer
    Pages 252-268
  15. T. A. Springer
    Pages 269-284
  16. T. A. Springer
    Pages 285-319
  17. Back Matter
    Pages 320-334

About this book

Introduction

"[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text."   –Mathematical Reviews (Review of the Second Edition)

"This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of the first ten chapters covers the contents of the old book, but the arrangement is somewhat different and there are additions, such as the basic facts about algebraic varieties and algebraic groups over a ground field, as well as an elementary treatment of Tannaka's theorem. These chapters can serve as a text for an introductory course on linear algebraic groups. The last seven chapters are new. They deal with algebraic groups over arbitrary fields. Some of the material has not been dealt with before in other texts, such as Rosenlicht's results about solvable groups in Chapter 14, the theorem of Borel and Tits on the conjugacy over the ground field of maximal split tori in an arbitrary linear algebraic group in Chapter 15, and the Tits classification of simple groups over a ground field in Chapter 17. The book includes many exercises and a subject index."   –Zentralblatt Math (Review of the Second Edition)

Keywords

Algebraic Geometry Borel Subgroups Commutative Algebraic Groups Derivation Lie Lie Theory Morphism Parabolic Subgroups The Isomorphism Theorem Weyl Groups algebra algebraic varieties geometry linear algebra theorem

Authors and affiliations

  • T. A. Springer
    • 1
  1. 1.Mathematisch InstituutRijksuniversiteit UtrechtUtrechtThe Netherlands

Bibliographic information