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Emergence of the Theory of Lie Groups

An Essay in the History of Mathematics 1869–1926

  • Book
  • © 2000

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Authors:
  1. Thomas Hawkins
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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiii
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  2. The Geometrical Origins of Lie’s Theory

    • Thomas Hawkins
    Pages 1-42

  3. Jacobi and the Analytical Origins of Lie’s Theory

    • Thomas Hawkins
    Pages 43-74

  4. Lie’s Theory of Transformation Groups: 1874–1893

    • Thomas Hawkins
    Pages 75-99

  5. The Background to Killing’s Work on Lie Algebras

    • Thomas Hawkins
    Pages 100-137

  6. Killing and the Structure of Lie Algebras

    • Thomas Hawkins
    Pages 138-181

  7. The Doctoral Thesis of Élie Cartan

    • Thomas Hawkins
    Pages 182-224

  8. Lie’s School and Linear Representations

    • Thomas Hawkins
    Pages 225-276

  9. Cartan’s Trilogy: 1913–14

    • Thomas Hawkins
    Pages 277-316

  10. The Göttingen School of Hilbert

    • Thomas Hawkins
    Pages 317-371

  11. The Berlin Algebraists: Frobenius and I. Schur

    • Thomas Hawkins
    Pages 372-419

  12. From Relativity to Representations

    • Thomas Hawkins
    Pages 420-464

  13. Weyl’s Great Papers of 1925 and 1926

    • Thomas Hawkins
    Pages 465-512

  14. Back Matter

    Pages 513-566
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Keywords

About this book

This book is both more and less than a history of the theory of Lie groups during the period 1869-1926. No attempt has been made to provide an exhaustive treatment of all aspects of the theory. Instead, I have focused upon its origins and upon the subsequent development of its structural as­ pects, particularly the structure and representation of semisimple groups. In dealing with this more limited subject matter, considerable emphasis has been placed upon the motivation behind the mathematics. This has meant paying close attention to the historical context: the mathematical or physical considerations that motivate or inform the work of a particular mathematician as well as the disciplinary ideals of a mathematical school that encourage research in certain directions. As a result, readers will ob­ tain in the ensuing pages glimpses of and, I hope, the flavor of many areas of nineteenth and early twentieth century geometry, algebra, and analysis. They will also encounter many of the mathematicians of the period, includ­ ing quite a few not directly connected with Lie groups, and will become acquainted with some of the major mathematical schools. In this sense, the book is more than a history of the theory of Lie groups. It provides a different perspective on the history of mathematics between, roughly, 1869 and 1926. Hence the subtitle.

Reviews

"....this study is just as clearly a stunning achievement. Few historians of mathematics have made a serious attempt to cross the bridge joining the nineteenth and twentieth centuries, and those who have made the journey have tended to avert their eyes from the mainstream traffic....the single greatest merit of Hawkins' book is that the author tries to place the reader in the middle of the action, offering a close up look at how mathematics gets made...Hawkins' account of this strange but wonderful saga resurrects a heroic chapter in the history of mathematics. For anyone with a serious interest in the rich background developments that led to modern Lie theory, this book should be browsed, read, savored, and read again."

-Notices of the AMS

Bibliographic Information

  • Book Title: Emergence of the Theory of Lie Groups

  • Book Subtitle: An Essay in the History of Mathematics 1869–1926

  • Authors: Thomas Hawkins

  • Series Title: Sources and Studies in the History of Mathematics and Physical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-1202-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 2000

  • Hardcover ISBN: 978-0-387-98963-1Published: 19 July 2000

  • Softcover ISBN: 978-1-4612-7042-3Published: 27 September 2012

  • eBook ISBN: 978-1-4612-1202-7Published: 06 December 2012

  • Series ISSN: 2196-8810

  • Series E-ISSN: 2196-8829

  • Edition Number: 1

  • Number of Pages: XIII, 566

  • Topics: Group Theory and Generalizations

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