Linear Algebra and Group Theory for Physicists pp 567-585 | Cite as

# 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*(*α*_{1} … *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.

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