Notes for AKT-170217/0:03:07: Difference between revisions
(Created page with "<math>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 <ma...") |
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Consider the algebra H obtained from <math>U(g_0)</math> by inverting h and quotienting by the relation <math>l=-ef/h</math> |
Consider the algebra H obtained from <math>U(g_0)</math> by inverting h and quotienting by the relation <math>l=-ef/h</math> |
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(check that <math>l+ef/h</math> is a central element in <math>U(g_0)</math>). And while we're at it, why not scale out the h entirely? |
(check that <math>l+ef/h</math> is a central element in <math>U(g_0)</math>). And while we're at it, why not scale out the h entirely? |
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Does H reproduce the theory of <math>\Gamma</math> calculus? |
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Also, the screen is impossible to see on video but the accompanying mathematica file makes up for it twice. |
Also, the screen is impossible to see on video but the accompanying mathematica file makes up for it twice. |
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{{Roland}} |
{{Roland}} |
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As for the screen, next time I'll lower the brightness level. --[[User:Drorbn|Drorbn]] ([[User talk:Drorbn|talk]]) 17:26, 17 February 2017 (EST) |
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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. --[[User:Drorbn|Drorbn]] ([[User talk:Drorbn|talk]]) 09:12, 20 February 2017 (EST) |
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Latest revision as of 13:17, 20 February 2017
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 by inverting h and quotienting by the relation (check that is a central element in ). And while we're at it, why not scale out the h entirely? Does H reproduce the theory of 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)
