Notes for AKT-170217/0:03:07

$g_{0}$ 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 $U(g_{0})$ by inverting h and quotienting by the relation $l=-ef/h$ (check that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle l+ef/h} is a central element in $U(g_{0})$). And while we're at it, why not scale out the h entirely? Does H reproduce the theory of $\Gamma$ 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)