Introduction to Compact Simple Lie Groups

Abstract

The purpose of this chapter is to give a brief and simple-minded introduction to Lie groups, and particularly compact simple Lie groups, since these are of considerable importance in particle physics, grand unification etc. The basic concepts of groups and group representations are assumed to be known — these include the definitions of a group, subgroup, normal subgroup, factor group, simple and semi-simple groups, Abelian and non-Abelian groups; homomorphisms and isomorphisms etc., irreducible representations, reducible decomposable or indecomposable representations, equivalence of representations, unitary and real ones, etc. Even while considering a group in the abstract, it helps to keep in mind some faithful matrix representations of it.