Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (2nd Edition)

By Brian C. Hall

Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Second Edition is a widely respected introduction to Lie theory designed for readers encountering the subject for the first time. Published by Springer, this book develops the essential ideas of Lie groups, Lie algebras, and representation theory with clear explanations and a strong emphasis on examples.

Ideal for advanced undergraduates and graduate students in mathematics and theoretical physics, the text builds intuition for matrix Lie groups, the exponential map, Lie algebra structure, basic representation theory, and key applications across geometry and quantum mechanics.

What This Book Does

This book provides a step-by-step foundation in Lie groups and Lie algebras and introduces representation theory in an accessible way, supporting both classroom learning and self-study.

Key Features of the 2nd Edition

• Accessible introduction with strong emphasis on matrix Lie groups
• Clear development of Lie algebras, the exponential map, and adjoint action
• Introductory representation theory with many worked examples
• Exercises that build technique and conceptual understanding
• Useful for mathematics, geometry, and theoretical physics students
• Widely adopted graduate-level introduction to Lie theory

Who Should Use This Book?

• Advanced undergraduate and graduate mathematics students
• Theoretical physics students (quantum mechanics, symmetry, gauge theory)
• Researchers needing a practical Lie theory reference
• Self-learners seeking an approachable introduction
• Courses on Lie groups, Lie algebras, and representation theory

Why It’s Essential

• One of the clearest elementary introductions to Lie theory
• Builds intuition with concrete matrix examples
• Connects algebra, geometry, and symmetry in a unified framework
• Strong foundation for advanced study in mathematics and physics

The trusted elementary introduction to Lie groups, Lie algebras, and representations.
Order today from BooksGoat and build your Lie theory foundation.

Product Details

• ISBN-13: 9783319134666
• Edition: 2nd
• Author: Brian C. Hall
• Publisher: Springer
• Format: Paperback
• Condition: New
• Availability: In Stock
• Shipping: Free Shipping

Table of Contents (Highlights)

• Matrix Lie Groups and Examples
• Lie Algebras and the Exponential Map
• Homomorphisms, Coverings, and the Adjoint Representation
• Representation Theory Basics
• Compact Lie Groups and Unitary Representations
• SU(2), SO(3), and Classical Examples
• Applications to Symmetry and Physics

FAQs

• Is this book suitable for beginners? Yes, it is designed as an elementary introduction with clear explanations and examples.
• Is it appropriate for graduate courses? Yes, it is widely used as a first graduate text in Lie theory.
• Does it include representation theory? Yes, it introduces representations and provides many illustrative examples.