# Talk:Affine Lie algebra

WikiProject Mathematics (Rated Start-class, Mid-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Start Class
 Mid Importance
Field: Algebra

The definition that Phys gave of affine Lie algebra, which today only exists in the page's history, is not unrelated. The affine Kac-Moody algebra described on the page is called affine because the Weyl group elements constructed using the imaginary root translate the codimension one part of the root space that is the root space of the corresponding finite-dimensional Lie group. That is, Kac-Moody affine algebras are called affine because their Weyl groups are affine in the traditional sense of the word. This is all explained in Kac's book. =JarahE

I am going to revamp this page. I find it to be wholly unacceptable. Myrkkyhammas 02:50, 26 April 2007 (UTC)

## Bracket

It seems the bracket should read ${\displaystyle [a\otimes t^{n}\oplus \alpha c,b\otimes t^{m}\oplus \beta c]=[a,b]\otimes t^{n}t^{m}+\langle a|b\rangle n\delta _{m+n,0}c}$ although it is harder to understand. Terminus0 (talk) 06:16, 17 November 2009 (UTC)

Good point. I rewrote it accordingly and cut out some clutter. Arcfrk (talk) 22:42, 17 November 2009 (UTC)