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Linear Algebraic Groups

  • Textbook
  • © 1991
  • Latest edition

Overview

Authors:
  1. Armand Borel

    1. School of Mathematics, Institute for Advanced Study, Princeton, USA

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  • Reprint of a successful expanded edition of a well-received book
  • Presents foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces
  • Requires only some familiarity with algebraic geometry

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

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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.

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Background Material from Algebraic Geometry

    • Armand Borel
    Pages 1-45

  3. General Notions Associated With Algebraic Groups

    • Armand Borel
    Pages 46-88

  4. Homogeneous Spaces

    • Armand Borel
    Pages 89-110

  5. Solvable Groups

    • Armand Borel
    Pages 111-146

  6. Borel Subgroups; Reductive Groups

    • Armand Borel
    Pages 147-202

  7. Rationality Questions

    • Armand Borel
    Pages 203-279

  8. Back Matter

    Pages 280-290
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Authors and Affiliations

  • School of Mathematics, Institute for Advanced Study, Princeton, USA

    Armand Borel

Bibliographic Information

  • Book Title: Linear Algebraic Groups

  • Authors: Armand Borel

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0941-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1991

  • Softcover ISBN: 978-1-4612-6954-0Published: 30 September 2012

  • eBook ISBN: 978-1-4612-0941-6Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XI, 290

  • Additional Information: Originally published by W.A. Benjamin, 1969

  • Topics: Topological Groups, Lie Groups

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