Talk:Kac–Moody algebra

More general
Aren't Kac-Moody algebras more general than this? Phys 01:59, 21 Nov 2004 (UTC)


 * I admit that it may be the case, but it still seems as a fine definition for 90% of our real purposes... --Lumidek 02:19, 21 Nov 2004 (UTC)


 * It's not even clear to me that this is even a Kac-Moody algebra. Which one is it? -- Walt Pohl 10:22, 30 Nov 2004 (UTC)


 * It's not a Kac-Moody algebra. It's simply the tensor product over [0,2&pi;) of a finite dimensional Lie algebra. Phys 03:55, 28 Dec 2004 (UTC)

cut-n-paste/loop algebra
I cut and pasted the following from the page, until I could determine its accuracy -- Walt Pohl 07:16, 2 Dec 2004 (UTC).

In abstract algebra and mathematical physics, a Kac-Moody algebra is an infinite-dimensional generalization of a Lie algebra. There are infinitely many generators in a Kac-Moody algebra that can be parameterized as $$L_i(\sigma)$$ where $$\sigma\in(0,2\pi)$$ parameterizes a circle and


 * $$[L_i(\sigma),L_j(\sigma')]=\delta(\sigma-\sigma') f_{ij}^k L_k$$

In string theory this algebra can be thought of as a copy of the original Lie algebra at each point of a closed string, and Kac-Moody algebras are also known as current algebras.


 * This descibes a loop algebra. An affine Kac-Moody algebra is a noncentral extension of the loop algebra over a semisimple Lie algebra, but not the loop algebra itself. This can be translated into the language of roots after we take a fourier transform. Phys 11:15, 28 Dec 2004 (UTC)

Disambiguation Fix
The link generator incorrectly links to a disambiguation page, my guess is that it should link to generator matrix or one of the articles listed in generator (mathematics). However I would appreciate it if someone a bit more knowledgeable on this subject can make the change. Thanks FlyHigh 12:54, 13 November 2006 (UTC)