Simple Lie Algebras

  • Philippe Di Francesco
  • Pierre Mathieu
  • David Sénéchal
Part of the Graduate Texts in Contemporary Physics book series (GTCP)


This chapter presents a survey of the theory of Lie algebras. This might appear somewhat remote from our main subject of interest: affine Lie algebras and their applications to conformal field theory. However, it turns out that in many respects the theory of affine Lie algebras is a natural extension of the theory of simple Lie algebras, and as such cannot be studied efficiently in isolation. This is an immediate motivation for devoting a complete chapter to Lie algebras. But as subsequent developments will show, conformal field theories with nonaffine additional symmetries, such as W algebras, parafermions, and son on, as well as related exactly solvable statistical models, also have a deep Lie-algebraic underlying structure, which can only be appreciated with a minimal background on simple Lie algebras.


Weyl Group Simple Root Dynkin Diagram Cartan Subalgebra Young Tableau 
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Copyright information

© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • Philippe Di Francesco
    • 1
  • Pierre Mathieu
    • 2
  • David Sénéchal
    • 3
  1. 1.Commissariat l’Énergie Atomique Centre d’Études de SaclayService de Physique ThéoriqueGif-sur-YvetteFrance
  2. 2.Département de PhysiqueUniversité LavalQuébecCanada
  3. 3.Département de PhysiqueUniversité de SherbrookeSherbrookeCanada

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