Representation Theory

Introduction

Representation theory is a branch of mathematics that studies abstract algebraic structures—like groups, associative algebras, and Lie algebras—by representing their elements as linear transformations acting on vector spaces. Essentially, it makes these abstract entities “concrete” via the familiar realm of linear algebra.

Contents

Representation of Finite Groups

Representation of Lie Algebras

Lie Algebra Representations

Projective Representations and Cohomology