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Matrix Groups

An Introduction to Lie Group Theory

  • Andrew¬†Baker

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Basic Ideas and Examples

    1. Front Matter
      Pages 1-1
    2. Andrew Baker
      Pages 3-43
    3. Andrew Baker
      Pages 67-97
    4. Andrew Baker
      Pages 129-156
    5. Andrew Baker
      Pages 157-178
  3. Matrix Groups as Lie Groups

    1. Front Matter
      Pages 179-179
    2. Andrew Baker
      Pages 181-209
    3. Andrew Baker
      Pages 211-233
    4. Andrew Baker
      Pages 235-247
  4. Compact Connected Lie Groups and their Classification

    1. Front Matter
      Pages 249-249
    2. Andrew Baker
      Pages 267-288
  5. Back Matter
    Pages 303-330

About this book

Introduction

Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter.
The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions.
Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry.

Keywords

Group theory Lie group Lie groups Matrix Matrix groups algebra differential geometry linear algebra

Authors and affiliations

  • Andrew¬†Baker
    • 1
  1. 1.Department of MathematicsUniversity of GlasgowGlasgowUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-0183-3
  • Copyright Information Springer-Verlag London Limited 2002
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-85233-470-3
  • Online ISBN 978-1-4471-0183-3
  • Series Print ISSN 1615-2085
  • Buy this book on publisher's site
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