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  • Textbook
  • © 1991

Linear Algebraic Groups

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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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  • ISBN: 978-1-4612-0941-6
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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xi
  2. Homogeneous Spaces

    • Armand Borel
    Pages 89-110
  3. Solvable Groups

    • Armand Borel
    Pages 111-146
  4. Borel Subgroups; Reductive Groups

    • Armand Borel
    Pages 147-202
  5. Rationality Questions

    • 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.

Keywords

  • Lie algebra
  • algebra
  • algebraic group
  • commutative algebra
  • linear algebra

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: 978-1-4612-6954-0

  • eBook ISBN: 978-1-4612-0941-6

  • 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 and Lie Groups

Buying options

eBook
USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-0941-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 69.99
Price excludes VAT (USA)