Welcome to MathOverflow

Question

3

2

What is a good reference for a fast approach to construct affine Kac-Moody algebras from finite-dimensional simple Lie algebras?

I know that Kac's book and many others do a very detailed and progressive construction, but I mean a understandable and direct realization as in the Hong and Kang's book about Quantum groups.

flag	asked Sep 15 2011 at 0:22 Chris 351●7

Bill Cook · Accepted Answer · 2011-09-15 20:01:25Z UTC

I am a big fan of Carter's book. It's very nicely laid out and I found it quite easy to read.

Here's an older reference: Kass, Moody, Patera, and Slansky's "Affine Lie Algebras, Weight Multiplicities, and Branching Rules"

This text is focused only on affine algebras. It is kind of light on proofs but provides a lot of nice details. Also, it's co-written by Physicists so there is an extra sprinkling of Physics flavor throughout.

Also, if you do decide to wade through Kac, you may want to pick up a copy of Minoru Wakimoto's "Infinite-Dimensional Lie Algebras" ISBN: 0821826549 (be careful Wakimoto has two books with almost the same exact title published at nearly the same time). Wakimoto's book makes a nice companion to Kac's book and is filled with great quotes such as: "sl2 representation theory is like Mt. Fuji reflected in a beautiful lake."

charris · Answer 2 · 2011-09-15 01:38:52Z UTC

5

I think you might like Affine Lie Algebras and Quantum Groups by Jurgen Fuchs. Also, Lie Algebras of Finite and Affine Type by Roger Carter is pretty good.

edited Sep 15 2011 at 1:38

answered Sep 15 2011 at 1:30

charris
521●3●8

affine Kac-Moody algebras

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

2 Answers

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.