Compact Lie Groups

  • Mark R. Sepanski

Part of the Graduate Texts in Mathematics book series (GTM, volume 235)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Pages 1-26
  3. Pages 27-46
  4. Pages 47-80
  5. Pages 81-95
  6. Pages 151-186
  7. Back Matter
    Pages 187-198

About this book


Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups. Included is the construction of the Spin groups, Schur Orthogonality, the Peter–Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and Character Formulas, the Highest Weight Classification, and the Borel–Weil Theorem. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups.

Key Features:

• Provides an approach that minimizes advanced prerequisites

• Self-contained and systematic exposition requiring no previous exposure to Lie theory

• Advances quickly to the Peter–Weyl Theorem and its corresponding Fourier theory

• Streamlined Lie algebra discussion reduces the differential geometry prerequisite and allows a more rapid transition to the classification and construction of representations

• Exercises sprinkled throughout


This beginning graduate-level text, aimed primarily at Lie Groups courses and related topics, assumes familiarity with elementary concepts from group theory, analysis, and manifold theory. Students, research mathematicians, and physicists interested in Lie theory will find this text very useful.


Group theory Lie algebra Representation theory algebra calculus differential geometry manifold maximum

Editors and affiliations

  • Mark R. Sepanski
    • 1
  1. 1.Department of MathematicsBaylor UniversityWacoUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-30263-8
  • Online ISBN 978-0-387-49158-5
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site