An Elementary Introduction to Groups and Representations

TL;DR

This paper provides an accessible introduction to Lie groups, Lie algebras, and their representations, covering fundamental concepts, examples, and specific cases like SU(3), suitable for graduate students in mathematics or physics.

Contribution

It offers an elementary, prerequisites-light overview of Lie groups and Lie algebras, including detailed analysis of SU(3) representations and a survey of semisimple groups' representation theory.

Findings

Detailed explanation of Lie group and algebra definitions

Explicit study of SU(3) representations

Survey of semisimple group representations

Abstract

These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions and examples of Lie groups and Lie algebras, the relationship between Lie groups and Lie algebras via the exponential mapping, the basics of representations theory, the Baker-Campbell-Hausdorff formula, a detailed study of the representations of SU(3), and a brief survey of the representation theory of general semisimple groups.