Advertisement

Introduction to the Classification of Lie Groups - Dynkin Diagram

  • K. N. Srinivasa Rao
Part of the Texts and Readings in Physical Sciences book series

Abstract

Since a careful presentation of Lie groups requires adequate preparation in topology which is beyond the scope of this short chapter whose purpose is only to give a brief introduction to the classification of Lie groups and Dynkin diagrams, we shall necessarily restrict ourselves just to the formalism of the theory and refer the reader to books* specially devoted to a study of topology and Lie groups. We shall thus accept the validity of the results for linear matrix groups provided in section (4-4) for more general Lie groups G whose elements g(α1α r ) are analytic functions of a finite number of parameters α k in a sufficiently small neighbourhood of the identity g(0, … 0). The number r of the parameters characterising the group is called the order of the group.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.E. Behrends, J. Dreitlein, C. Fronsdal and W. Lee, Simple Groups and Strong Interaction Symmetries, Rev. Mod. Phys. 34, 1 (1962).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    E.B. Dynkin, Appendix to Maximal Subgroups of the Classical Groups, Amer. Math. Soc. Transl. II, 6, 17 (1950).Google Scholar
  3. 3.
    S. Mukhi and N. Mukunda, Introduction to Topology, Differential Geometry and Group Theory for Physicists, Wiley Eastern Limited, New Delhi, 1990.zbMATHGoogle Scholar
  4. 4.
    G. Racah, Group Theory and Spectroscopy, CERN Report 61–8, p69, 1961.Google Scholar
  5. 5.
    A. Salam, The Formalism of Lie Groups, Trieste Seminar 1963Google Scholar
  6. 6.
    B.G. Wybourne, Classical Groups for Physicists, Wiley, New York, 1974.zbMATHGoogle Scholar

Copyright information

© Hindustan Book Agency 2006

Authors and Affiliations

  • K. N. Srinivasa Rao
    • 1
  1. 1.BangaloreIndia

Personalised recommendations