affine Kac-Moody algebras - MathOverflow

affine Kac-Moody algebras

2011-09-15T00:22:11Z

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.

Answer by charris for affine Kac-Moody algebras

2011-09-15T01:30:44Z

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.

Answer by Bill Cook for affine Kac-Moody algebras

2011-09-15T20:01:25Z

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."