Timeline for Recovering a Lie algebra from its affine Lie algebra

8 events

when toggle format	what		by	license	comment
May 11, 2013 at 9:45	answer	added	Pasha Zusmanovich		timeline score: 1
May 25, 2012 at 3:57	answer	added	S. Carnahan♦		timeline score: 2
May 24, 2012 at 20:07	comment	added	H. Arponen		I'm assuming you just have the Lie algebra as commutation relations, maybe due to some symmetries of PDEs or such, and you're trying to determine if it corresponds to an affine Lie algebra?
May 24, 2012 at 16:34	history	edited	Eric O. Korman	CC BY-SA 3.0	added 35 characters in body
May 24, 2012 at 15:34	answer	added	Jim Humphreys		timeline score: 0
May 24, 2012 at 15:30	comment	added	Bill Cook		However, an affine algebra $\hat{\mathfrak{g}}$ carries more information than just its Lie algebra structure. It has a built in gradation: $\hat{\mathfrak{g}}(n) = \mathfrak{g} \otimes t^n$. If you have this information, then your problem is trivial since $\hat{\mathfrak{g}}(0) = \mathfrak{g}$.
May 24, 2012 at 15:29	comment	added	Bill Cook		This is what comes to mind: If you can find a cartan subalgebra (CSA), then $\hat{\mathfrak{g}}$ decomposes into root spaces. Take a maximal collection $\Delta$ of real roots such that the sum of any two elements of $\Delta$ is either in $\Delta$, 0, or not a root. Then the direct sum of the root spaces associated with the roots in $\Delta$ along with the CSA will give you $\mathfrak{g}$.
May 24, 2012 at 14:59	history	asked	Eric O. Korman	CC BY-SA 3.0