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Naive Lie Theory

  • John¬†Stillwell

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. John Stillwell
    Pages 23-47
  3. John Stillwell
    Pages 48-73
  4. John Stillwell
    Pages 74-92
  5. John Stillwell
    Pages 93-115
  6. John Stillwell
    Pages 116-138
  7. John Stillwell
    Pages 139-159
  8. John Stillwell
    Pages 160-185
  9. John Stillwell
    Pages 186-203
  10. Back Matter
    Pages 204-218

About this book

Introduction

In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra.

This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history.

John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).

Keywords

Matrix Symmetry group algebra lie algebra lie group linear algebra matrices number theory

Authors and affiliations

  • John¬†Stillwell
    • 1
  1. 1.University of San FranciscoDepartment of MathematicsSan FranciscoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-78214-0
  • Copyright Information Springer Science+Business Media, LLC 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-78214-0
  • Online ISBN 978-0-387-78215-7
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site