affine Kac-Moody algebras - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T02:14:24Z http://mathoverflow.net/feeds/question/75464 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/75464/affine-kac-moody-algebras affine Kac-Moody algebras Chris 2011-09-15T00:22:11Z 2011-09-15T20:01:25Z <p>What is a good reference for a fast approach to construct affine Kac-Moody algebras from finite-dimensional simple Lie algebras? </p> <p>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.</p> http://mathoverflow.net/questions/75464/affine-kac-moody-algebras/75469#75469 Answer by charris for affine Kac-Moody algebras charris 2011-09-15T01:30:44Z 2011-09-15T01:38:52Z <p>I think you might like <a href="http://books.google.com/books?id=ckZ-jfbqEbgC&amp;lpg=PP1&amp;dq=fuchs%2520affine%2520algebras&amp;pg=PR9#v=onepage&amp;q&amp;f=false" rel="nofollow">Affine Lie Algebras and Quantum Groups</a> by Jurgen Fuchs. Also, <a href="http://books.google.com/books?id=gv2Xf8VVi2MC&amp;lpg=PP1&amp;dq=carter%2520lie%2520algebras&amp;pg=PP1#v=onepage&amp;q&amp;f=false" rel="nofollow">Lie Algebras of Finite and Affine Type</a> by Roger Carter is pretty good.</p> http://mathoverflow.net/questions/75464/affine-kac-moody-algebras/75555#75555 Answer by Bill Cook for affine Kac-Moody algebras Bill Cook 2011-09-15T20:01:25Z 2011-09-15T20:01:25Z <p>I am a big fan of Carter's book. It's very nicely laid out and I found it quite easy to read.</p> <p>Here's an older reference: Kass, Moody, Patera, and Slansky's "Affine Lie Algebras, Weight Multiplicities, and Branching Rules"</p> <p>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.</p> <p>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."</p>