Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics

  • D. H. Sattinger
  • O. L. Weaver

Part of the Applied Mathematical Sciences book series (AMS, volume 61)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Lie Groups and Algebras

    1. Front Matter
      Pages 1-1
    2. D. H. Sattinger, O. L. Weaver
      Pages 3-20
    3. D. H. Sattinger, O. L. Weaver
      Pages 21-31
    4. D. H. Sattinger, O. L. Weaver
      Pages 32-40
    5. D. H. Sattinger, O. L. Weaver
      Pages 41-54
  3. Differential Geometry and Lie Groups

    1. Front Matter
      Pages 55-55
    2. D. H. Sattinger, O. L. Weaver
      Pages 57-75
    3. D. H. Sattinger, O. L. Weaver
      Pages 76-88
    4. D. H. Sattinger, O. L. Weaver
      Pages 89-108
    5. D. H. Sattinger, O. L. Weaver
      Pages 109-115
  4. Algebraic Theory

    1. Front Matter
      Pages 117-117
    2. D. H. Sattinger, O. L. Weaver
      Pages 119-129
    3. D. H. Sattinger, O. L. Weaver
      Pages 130-152
    4. D. H. Sattinger, O. L. Weaver
      Pages 153-159
  5. Representation Theory

    1. Front Matter
      Pages 161-161
    2. D. H. Sattinger, O. L. Weaver
      Pages 163-180
    3. D. H. Sattinger, O. L. Weaver
      Pages 181-186
  6. Applications

    1. Front Matter
      Pages 187-187
    2. D. H. Sattinger, O. L. Weaver
      Pages 189-207

About this book

Introduction

This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo­ metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym­ metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications­ oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.

Keywords

Algebra Algebras Applications Geometry Groups Mechanics Physics Representation theory Symmetry group

Authors and affiliations

  • D. H. Sattinger
    • 1
  • O. L. Weaver
    • 2
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of PhysicsKansas State UniversityManhattanUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-1910-9
  • Copyright Information Springer-Verlag New York 1986
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3077-4
  • Online ISBN 978-1-4757-1910-9
  • Series Print ISSN 0066-5452
  • About this book
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