Looking for a new Lie Algebra text

In summary, the conversation discusses the frustration of using the book "Affine Lie Algebras and Quantum Groups" by Fuchs for studying Lie algebras. The book presents a construction of two vector spaces, L and Lw, where Lw is dual to L. However, the text states that L is a subset of Lw, which is not possible for dual spaces. The next paragraph explains how to interpret this, but the speaker is still dissatisfied with the presentation. They ask for recommendations for a better Lie algebra text, preferably with a focus on physics.
  • #1
topsquark
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Right now I'm using "Affine Lie Algebras and Quantum Groups" by Fuchs. I'm getting sick of it. As a Physicist the structure and focus of the text is attractive to me. But, to give one example...

The text constructs two vector spaces: L and Lw. Lw is dual to L. The text goes on to state that \(\displaystyle L \subset Lw\). As the two spaces are dual this cannot be.

BUT: The next paragraph shows how to interpret this. We can (apparently) define a metric between the two spaces and if we use the metric to compare the space dual to L to Lw then we find that L is a subspace of Lw which given the definitions of both spaces is a completely banal comment and isn't actually needed.

I can't take this kind of presentation any more!

Does anyone know of a decent Lie algebra text? I would appreciate with a Physics bent, but that isn't necessary.

Thanks!

-Dan
 
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  • #2
About a year ago, I posted recommendations for books on lie groups/lie algebras http://mathhelpboards.com/linear-abstract-algebra-14/looking-online-algebra-resource-12409.html#post59081. Have you taken a look at any of the two? If you're not satisfied with those two then I can give you some more recommendations.
 
  • #3
Euge said:
About a year ago, I posted recommendations for books on lie groups/lie algebras http://mathhelpboards.com/linear-abstract-algebra-14/looking-online-algebra-resource-12409.html#post59081. Have you taken a look at any of the two? If you're not satisfied with those two then I can give you some more recommendations.
Gah! I forgot I did that. Sorry!

I'll take a fresh look at the list. Thanks!

-Dan
 

Related to Looking for a new Lie Algebra text

1. What is a Lie Algebra?

A Lie Algebra is a mathematical concept that studies the properties and structures of vector spaces equipped with a binary operation called the Lie bracket. It is used to study continuous symmetries and is closely related to the field of differential equations.

2. Why do I need a new Lie Algebra text?

As a scientist, it is important to constantly update and expand your knowledge in your field. A new Lie Algebra text can provide new insights, approaches, and applications of this mathematical concept. It can also update your understanding of the subject and keep you up-to-date with current research.

3. What should I look for in a Lie Algebra text?

When searching for a new Lie Algebra text, it is important to consider the author's expertise and credibility, the level of mathematical rigor, and the inclusion of relevant examples and applications. It is also helpful to read reviews and recommendations from other mathematicians or scientists in the field.

4. Are there any recommended Lie Algebra texts?

There are many highly recommended Lie Algebra texts, such as "Introduction to Lie Algebras and Representation Theory" by Humphreys, "Lie Algebras, Part 1" by Serre, and "Lie Algebras and Their Representations" by Varadarajan. It is important to choose a text that best fits your level of understanding and purpose for studying Lie Algebras.

5. How can I use a Lie Algebra text in my research?

Lie Algebras have applications in various fields such as physics, chemistry, and mathematics. By studying a new Lie Algebra text, you can expand your understanding of this concept and potentially apply it to your own research. The text can also serve as a reference for specific techniques and properties related to Lie Algebras.

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