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Basic Theory of Algebraic Groups and Lie Algebras

  • Gerhard P. Hochschild

Part of the Graduate Texts in Mathematics book series (GTM, volume 75)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Gerhard P. Hochschild
    Pages 1-14
  3. Gerhard P. Hochschild
    Pages 15-27
  4. Gerhard P. Hochschild
    Pages 28-43
  5. Gerhard P. Hochschild
    Pages 44-58
  6. Gerhard P. Hochschild
    Pages 59-77
  7. Gerhard P. Hochschild
    Pages 78-92
  8. Gerhard P. Hochschild
    Pages 93-105
  9. Gerhard P. Hochschild
    Pages 106-121
  10. Gerhard P. Hochschild
    Pages 122-136
  11. Gerhard P. Hochschild
    Pages 137-154
  12. Gerhard P. Hochschild
    Pages 155-172
  13. Gerhard P. Hochschild
    Pages 173-187
  14. Gerhard P. Hochschild
    Pages 188-199
  15. Gerhard P. Hochschild
    Pages 200-209
  16. Gerhard P. Hochschild
    Pages 210-220
  17. Gerhard P. Hochschild
    Pages 221-232
  18. Gerhard P. Hochschild
    Pages 233-248
  19. Gerhard P. Hochschild
    Pages 249-262
  20. Back Matter
    Pages 263-270

About this book

Introduction

The theory of algebraic groups results from the interaction of various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras. It is thus an ideally suitable framework for exhibiting basic algebra in action. To do that is the principal concern of this text. Accordingly, its emphasis is on developing the major general mathematical tools used for gaining control over algebraic groups, rather than on securing the final definitive results, such as the classification of the simple groups and their irreducible representations. In the same spirit, this exposition has been made entirely self-contained; no detailed knowledge beyond the usual standard material of the first one or two years of graduate study in algebra is pre­ supposed. The chapter headings should be sufficient indication of the content and organisation of this book. Each chapter begins with a brief announcement of its results and ends with a few notes ranging from supplementary results, amplifications of proofs, examples and counter-examples through exercises to references. The references are intended to be merely suggestions for supplementary reading or indications of original sources, especially in cases where these might not be the expected ones. Algebraic group theory has reached a state of maturity and perfection where it may no longer be necessary to re-iterate an account of its genesis. Of the material to be presented here, including much of the basic support, the major portion is due to Claude Chevalley.

Keywords

Algebraische Gruppe Basic Groups Lie Lie algebra Liesche Algebra algebra algebraic group automorphism cohomology commutative ring group theory homology representation theory ring theory

Authors and affiliations

  • Gerhard P. Hochschild
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8114-3
  • Copyright Information Springer-Verlag New York 1981
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-8116-7
  • Online ISBN 978-1-4613-8114-3
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site