3

I am looking for a book talking about Lie groups and Lie algebras but not in a too abstract way.

In fact I am doing physics and I need to understand the structure of Lie algebras : why are elements of a group exponential of the algebra, why is the Lie group the tangent space etc.

I studied groups representation with the book "HF Jones Group representation and physics" and I am looking for a book like this one but talking about Lie groups & Lie algebra.

To give you an idea, I liked this book because it gave physical motivations before introducing the representations of groups, because it has proof and it is not written in a too abstract way, it has corrected exercices. Also it did some reminder on Algebra, Group theory before starting : it doesn't assume a perfect background before starting. And it goes in a straight way, it doesn't say thousands of theorem but it just expose what is necessary to get the main point.

StarBucK
  • 689
  • I studied from this one – caverac May 16 '17 at 11:14
  • What's wrong with abstract for physicist? Have you read Andrew Lisi's Exceptionally simple E8 theory of everything? Which makes use of lie algebras? – marshal craft May 16 '17 at 11:27
  • What I want to say is I don't want to go into deep maths because I just need to understand the structure of it. I have read book on representations theory that are really hard to understand before I read the HF Jones. – StarBucK May 16 '17 at 11:39
  • 1
    @marshall: I don't think we should say "You're asking the wrong question" unless there's a principled reason for it (as in "you can't ask us to find three solutions to a quadratic over the reals!"). Some physicists may love abstraction; others may need to know some Lie theory for more prosaic reasons in which the abstraction is a burden to them. – John Hughes May 16 '17 at 12:32
  • I highly recommend studying at least the structure theory of complex semisimple Lie algebras. It is just an amazing theorem, the classification theorem, using root systems. As far as recommendations, I would recommend for instance Wolfgang Ziller's lecture notes, which have a geometric flavor. Not sure about the Physically inclined lecture notes, but you could try browsing on say the Cambridge, or MIT, or... websites. – Malkoun May 16 '17 at 14:50
  • W. Ziller's notes can be found here: https://www.math.upenn.edu/~wziller/math650/LieGroupsReps.pdf – Malkoun May 16 '17 at 14:54
  • Thank you for your reccomendation, but it is not exactly what i am looking for. Indeed it is written "for mathematician", I mean that it needs a background to be fully understandable. Also it is very dense. The book I used to learn representations of group for example do some reminders on group theory, algebra etc before starting. I am looking for such a book. – StarBucK May 17 '17 at 09:56
  • I'm surprised no one has mentioned books by Robert Hermann. Indeed, for a while (late 1960s through the 1970s) it seemed he was writing a book every few months (most are probably listed here). Anyway, his first book is Lie Groups for Physicists (internet archive version), but many of his later books might also be of interest, such as his 2-volume "Lectures in Mathematical Physics" (see here. – Dave L. Renfro Jan 16 '24 at 08:32
  • I just realized this question is from over 6.5 years ago. For some reason it was bumped to the top of the question queue, and I didn't notice the date until after I posted my comment. However, maybe the comment will be of use to others. For what it's worth, I don't know to what extent Hermann's books might be useful (not my area of expertise), but Hermann definitely played up his books in the many spirited prefaces he wrote for his books (I enjoyed reading his prefaces back in the late 1970s when I was an undergraduate student). – Dave L. Renfro Jan 16 '24 at 08:36

1 Answers1

1

You might want to check out the textbook Quantum Theory, Groups, and Representations: An Introduction by Peter Woit. The PDF is available on his website:

http://www.math.columbia.edu/~woit/

Maybe also Naive Lie Theory by Stillwell is worth a look:

https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Mathematics/dp/144192681X

littleO
  • 51,938