Talk:Affine Lie algebra

Untitled

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 $[a\otimes t^{n}\oplus \alpha c,b\otimes t^{m}\oplus \beta c]=[a,b]\otimes t^{n}t^{m}+\langle a|b\rangle n\delta _{m+n,0}c$ 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)

Basis for vacuum representation

The listed basis for the vacuum representation requires the affine vertex algebra article to be well defined, as it involves a product of vectors of a representation, which do not (a priori) have a well defined multiplicative structure.

I do not know how to fix this problem. 2601:184:497F:8A90:69B5:800D:8539:A82D (talk) 03:13, 19 August 2024 (UTC)