Introductory book on Lie Groups?

In summary, the conversation discusses the search for an introductory book on Lie Groups and Lie Algebras with a focus on understanding, applications, and examples rather than proofs. Suggestions include "Lie Groups for Pedestrians" by John Stillwell, "Lie Groups, Lie Algebras, and Some of Their Applications" by Robert Gilmore, and Brian Hall's book which is pure math but does not require any knowledge of differential geometry.
  • #1
nicksauce
Science Advisor
Homework Helper
1,271
7
Hi. I'm looking for an introductory book on Lie Groups and Lie Algebras and their applications in physics. Preferably the kind of book that emphasizes understanding, applications and examples, rather than proofs. Any suggestions?

Edit: Please move this to Science Book Discussion.
 
Last edited:
Physics news on Phys.org
  • #2
The first introduction I read on Lie groups was Lie Groups for Pedestrians. It's short, cheap, easy to read, and presumes no more knowledge than knowing about angular momentum algebra in quantum mechanics.
 
  • #4
I like:: Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore.
It's only $20 in paperback through Amazon.
 
  • #5
Brian Hall's book is nice. It's pure math, but it doesn't require any differential geometry. It doesn't contain any applications to physics.
 

1. What is a Lie group?

A Lie group is a mathematical concept that combines the ideas of a group (a set with a binary operation) and a smooth manifold (a space that locally resembles Euclidean space). Essentially, it is a group that also has a well-defined notion of continuity and differentiability.

2. Why are Lie groups important?

Lie groups have many applications in mathematics and physics, particularly in the fields of geometry, topology, and theoretical physics. They provide a powerful tool for understanding the symmetries of a system and have been used to study a wide range of phenomena, including the behavior of particles in quantum mechanics and the geometry of curved spaces.

3. What are some examples of Lie groups?

Some common examples of Lie groups include the general linear group, special linear group, orthogonal group, and unitary group. Other examples include the rotation group in three dimensions, the Lorentz group in special relativity, and the symplectic group in classical mechanics.

4. How are Lie groups related to Lie algebras?

Lie groups and Lie algebras are closely related mathematical structures. A Lie algebra is a vector space equipped with a bilinear operation (called the Lie bracket) that satisfies certain properties. Lie groups and Lie algebras are related through a process called exponential mapping, which allows for the translation of algebraic properties of the Lie algebra to geometric properties of the Lie group.

5. Is knowledge of abstract algebra necessary to understand Lie groups?

While a basic understanding of abstract algebra can be helpful in understanding Lie groups, it is not strictly necessary. Many introductory books on Lie groups are written in a way that assumes little prior knowledge of abstract algebra, focusing instead on the geometric and physical aspects of the subject.

Similar threads

  • Science and Math Textbooks
Replies
6
Views
1K
  • Science and Math Textbooks
Replies
5
Views
1K
  • Science and Math Textbooks
Replies
5
Views
1K
  • Science and Math Textbooks
Replies
18
Views
2K
  • Science and Math Textbooks
Replies
14
Views
2K
  • Science and Math Textbooks
Replies
4
Views
1K
  • Science and Math Textbooks
Replies
4
Views
3K
  • Science and Math Textbooks
Replies
1
Views
1K
  • Science and Math Textbooks
Replies
4
Views
1K
  • Science and Math Textbooks
Replies
18
Views
2K
Back
Top