Comparing Books on Lie Groups: Representations & Compact Lie Groups

In summary, during a conversation about Lie Groups and Representations, the topic of recommended books was brought up. The individual mentioned using the book "Representations of compact Lie Groups" but found it to be disorganized. They asked for suggestions on a clear and rigorous book, and also mentioned their background in manifolds and Riemannian geometry. They then mentioned the book "Compact Lie Groups" by Sepanski and asked for comments on it. Another individual suggested looking at books by experts such as Chevalley, Weyl, and Serre, which may be more condensed but well-organized and authoritative. Links to previous discussions on this topic were also provided.
  • #1
mrandersdk
246
1
I'm taking a course on Lie Groups and the Representations. We are using the book: Representations of compact Lie Groups by Bröcker and Dieck, and I find it very unorganized and sometimes sloppy. Can anybody recommend a very clear and rigorous book, where it is not prove by example, "it is easily seen", etc.

I have taking a course on manifolds and riemannian geometry so I'm not a complete novice in the field of differential geometry.

I've been thinking about the book Compact Lie Groups by Sepanski, anybody got a comment on this book?

Thanks in advance.
 
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  • #2
I know next to nothing about the topic, but I am a professional mathematician and thus understand the value of expert treatments.

hence i would suggest looking at the books by great experts like chevalley, weyl, serre.

such books tend to be hard and condensed , but well organized and authoritative.
 

Related to Comparing Books on Lie Groups: Representations & Compact Lie Groups

1. What is the main focus of "Comparing Books on Lie Groups: Representations & Compact Lie Groups"?

The main focus of this book is to provide a comprehensive understanding of the theory of Lie groups, representations, and compact Lie groups. It compares different approaches and perspectives on these topics, allowing readers to gain a deeper insight into the subject.

2. How is this book different from other books on Lie groups and representations?

This book offers a unique perspective by comparing different books on Lie groups and representations. It not only presents the theories, but also discusses the strengths and weaknesses of each approach, providing a more well-rounded understanding of the subject.

3. What level of knowledge is required to understand this book?

This book is suitable for advanced undergraduate or graduate students in mathematics, physics, or engineering who have a basic understanding of group theory, linear algebra, and calculus. It may also be useful for researchers and professionals in the field.

4. Are there any prerequisites for reading this book?

Readers should have a solid foundation in mathematics, including group theory, linear algebra, and calculus. Familiarity with topics such as differential geometry and representation theory may also be helpful, but not necessary.

5. What are some key topics covered in this book?

Some key topics covered in this book include Lie groups and algebras, representations of Lie groups, compact Lie groups and their representations, and the relationships between different approaches to studying Lie groups and representations. It also includes applications to physics and other fields.

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