Introduction to Lie Groups?

In summary, Aditya is looking for introductory material on Lie groups and their connections with differential geometry, but does not want to get too involved in physics. Carter Segal Macdonald's "Lectures on Lie Groups and Lie Algebras" and Michael Artin's "Algebra" are both recommended as good resources for beginners in this topic.
  • #1
adityatatu
15
0
Hi all,
I wanted to study Lie groups and their connections with differential geometry. But i don't want to get involved with lots of 'deep physics'.
I am familiar with a little bit of group theory.
can somebody suggest the right introductory material like tutorial papers or books for such a study?
thanks in advance.
Aditya
http://www.geocities.com/aditya_tatu
 
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  • #2
Carter Segal Macdonald, LMS Text, Lectures on Lie Groups and Lie Algebras.

No introductory pure mathematics text will deal with phsysics.
 
  • #3
algebra, by michael artin, has a couple chapters on the most elementary examples of lie groups, and representations, like the double cover of SO(3) by SU(2). This was written for sophomore abstract algebra beginners (at MIT).
 

1. What is a Lie group?

A Lie group is a type of mathematical group that is also a smooth manifold. It is a group in the sense that it has a group operation, and it is a manifold in the sense that it can be described locally by coordinates.

2. What is the significance of Lie groups in mathematics and science?

Lie groups are important in many areas of mathematics and science, including physics, geometry, and differential equations. They provide a way to study symmetries and continuous transformations, making them useful in understanding the underlying structure of physical systems and solving problems in various fields.

3. What is the relationship between Lie groups and Lie algebras?

Lie algebras are a type of algebraic structure that is closely related to Lie groups. Every Lie group has an associated Lie algebra, and the study of Lie algebras can provide insights into the structure of Lie groups.

4. Can you give an example of a Lie group?

One example of a Lie group is the general linear group, which consists of all invertible matrices of a given size. This group is important in linear algebra and has applications in physics, such as in the study of quantum mechanics.

5. What are some real-world applications of Lie groups?

Lie groups have many applications in physics, including in the study of particle physics, relativity, and differential geometry. They are also used in robotics and computer vision for motion planning and object recognition. Additionally, Lie groups have applications in coding theory, cryptography, and other areas of mathematics and computer science.

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