Skip to main content
SpringerLink
Log in

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

  • Book
  • © 1986

Overview

Authors:
  1. D. H. Sattinger

    1. School of Mathematics, University of Minnesota, Minneapolis, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. O. L. Weaver

    1. Department of Physics, Kansas State University, Manhattan, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (14 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Lie Groups and Algebras

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Lie Groups

      • D. H. Sattinger, O. L. Weaver
      Pages 3-20

    3. Lie Algebras

      • D. H. Sattinger, O. L. Weaver
      Pages 21-31

    4. Lie Groups and Algebras: Matrix Approach

      • D. H. Sattinger, O. L. Weaver
      Pages 32-40

    5. Applications to Physics and Vice Versa

      • D. H. Sattinger, O. L. Weaver
      Pages 41-54

  3. Differential Geometry and Lie Groups

    1. Front Matter

      Pages 55-55
      Download chapter PDF

    2. Calculus on Manifolds

      • D. H. Sattinger, O. L. Weaver
      Pages 57-75

    3. Symmetry Groups of Differential Equations

      • D. H. Sattinger, O. L. Weaver
      Pages 76-88

    4. Invariant Forms on Lie Groups

      • D. H. Sattinger, O. L. Weaver
      Pages 89-108

    5. Lie Groups and Algebras: Differential Geometric Approach

      • D. H. Sattinger, O. L. Weaver
      Pages 109-115

  4. Algebraic Theory

    1. Front Matter

      Pages 117-117
      Download chapter PDF

    2. General Structure of Lie Algebras

      • D. H. Sattinger, O. L. Weaver
      Pages 119-129

    3. Structure of Semi-Simple Lie Algebras

      • D. H. Sattinger, O. L. Weaver
      Pages 130-152

    4. Real Forms

      • D. H. Sattinger, O. L. Weaver
      Pages 153-159

  5. Representation Theory

    1. Front Matter

      Pages 161-161
      Download chapter PDF

    2. Representation Theory

      • D. H. Sattinger, O. L. Weaver
      Pages 163-180

    3. Spinor Representations

      • D. H. Sattinger, O. L. Weaver
      Pages 181-186

  6. Applications

    1. Front Matter

      Pages 187-187
      Download chapter PDF

    2. Applications

      • D. H. Sattinger, O. L. Weaver
      Pages 189-207
Back to top

Keywords

About this book

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 themselvesto 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.

Authors and Affiliations

  • School of Mathematics, University of Minnesota, Minneapolis, USA

    D. H. Sattinger

  • Department of Physics, Kansas State University, Manhattan, USA

    O. L. Weaver

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation