Complex Semisimple Lie Algebras

  • Jean-Pierre Serre

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages N1-ix
  2. Jean-Pierre Serre
    Pages 5-9
  3. Jean-Pierre Serre
    Pages 10-16
  4. Jean-Pierre Serre
    Pages 24-42
  5. Jean-Pierre Serre
    Pages 43-55
  6. Jean-Pierre Serre
    Pages 66-71
  7. Back Matter
    Pages 72-75

About this book


These short notes, already well-known in their original French edition, give the basic theory of semisimple Lie algebras over the complex numbers, including classification theorem. The author begins with a summary of the general properties of nilpotent, solvable, and semisimple Lie algebras. Subsequent chapters introduce Cartan subalgebras, root systems, and linear representations. The last chapter discusses the connection between Lie algebras, complex groups and compact groups; it is intended to guide the reader towards further study.


Lie algebra Lie algebras Matrix Representation theory algebra group theory

Authors and affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Collège de FranceParis Cedex 05France

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63222-8
  • Online ISBN 978-3-642-56884-8
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site