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Introduction to the Theory of Lie Groups

  • Textbook
  • © 2017

Overview

Authors:
  1. Roger Godement

    1. Paris, France

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  • Written in the author’s inimitable style
  • Includes full background on topological groups and group quotients
  • Contains many exercises and concrete examples
  • Requires only basic knowledge of topology and algebra
  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Topological Groups

    • Roger Godement
    Pages 1-32

  3. Simply Connected Spaces and Groups

    • Roger Godement
    Pages 33-60

  4. Analytic Properties of Linear Groups

    • Roger Godement
    Pages 61-112

  5. Manifolds and Lie Groups

    • Roger Godement
    Pages 113-140

  6. The Lie Algebra of a Lie Group

    • Roger Godement
    Pages 141-227

  7. The Exponential Map for Lie Groups

    • Roger Godement
    Pages 229-283

  8. Back Matter

    Pages 285-293
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Keywords

About this book

This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory.


Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.

Reviews

“The book draws many very interesting connections, say to topological groups, that are rarely found in more recent books. Hence I believe it is a valuable source for material for courses on the topic.” (A. Cap, Monatshefte für Mathematik, Vol. 192 (4), August, 2020)

“This book is an educational text, in which practically all statements, which are contained in it, are proved. Therefore it is written for students, who want not only to study the theory of Lie groups and Lie algebras and to pass an examination, but to study the foundation of Lie theory for effectively using it in further scientific work.” (V. V. Gorbatsevich, zbMATH 1367.22001, 2017)


Authors and Affiliations

  • Paris, France

    Roger Godement

About the author

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on abstract algebra and mathematical analysis.

Bibliographic Information

  • Book Title: Introduction to the Theory of Lie Groups

  • Authors: Roger Godement

  • Translated by: Urmie Ray

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-319-54375-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Softcover ISBN: 978-3-319-54373-4Published: 13 May 2017

  • eBook ISBN: 978-3-319-54375-8Published: 09 May 2017

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: IX, 293

  • Topics: Topological Groups, Lie Groups

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