Notes for AKT-170217/0:03:07

[math]\displaystyle{ g_0 }[/math] may be the 0th in the class of Lie algebras we're playing with but its enveloping algebra can be made simpler still. Consider the algebra H obtained from [math]\displaystyle{ U(g_0) }[/math] by inverting h and quotienting by the relation [math]\displaystyle{ l=-ef/h }[/math] (check that [math]\displaystyle{ l+ef/h }[/math] is a central element in [math]\displaystyle{ U(g_0) }[/math]). And while we're at it, why not scale out the h entirely? Does H reproduce the theory of [math]\displaystyle{ \Gamma }[/math] calculus? Also, the screen is impossible to see on video but the accompanying mathematica file makes up for it twice. Roland

As for the screen, next time I'll lower the brightness level. --Drorbn (talk) 17:26, 17 February 2017 (EST)

Incidentally, the fact that $l+ef/h$ is central is really that $hl+ef$ is central, which follows from the fact that $h\otimes l+e\otimes f=h_1l_2+e_1f_2$ is invariant, by stitching using $m^{12}_1$. But the invariance of $h\otimes l+e\otimes f$ is the standard "invariance of a chord", or "invariance of the Casimir", and moding out by it is imposing the "Framing Independence" relation. --Drorbn (talk) 09:12, 20 February 2017 (EST)