Symmetry, matrix lie groups their lie algebras and representations

Abstract

In this project work, we first become familiar with rigid motions and symmetry, discuss a result stating all possibilities for a finite subgroup of SO3. We further study free groups to understand the structure of finite groups using Todd Coxeter Algorithm. The matrix Lie group, matrix exponential map and its existence have also been discussed. Further, we have studied the Lie algebras of the matrix Lie groups. In the last chapter, we study some examples of representations of the matrix Lie groups and their Lie algebras. The last result is about the completely reducibility of a compact matrix Lie group.