Introduction to the Classification of Lie Groups - Dynkin Diagram

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(α₁ … α _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.