06-1350/Class Notes for Tuesday November 14 - Revision history

Drorbn at 14:17, 15 November 2006

2006-11-15T14:17:52Z

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	{{06-1350/Navigation}}		{{06-1350/Navigation}}

	{{In Preparation}}

	==Today's Agenda==		==Today's Agenda==

Drorbn at 14:17, 15 November 2006

2006-11-15T14:17:44Z

← Older revision		Revision as of 10:17, 15 November 2006
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	* Finish describing the necessary relations between <math>T</math>, <math>R</math>, <math>\Phi</math> and <math>B^{\pm}</math> in verbal form.		* Finish describing the necessary relations between <math>T</math>, <math>R</math>, <math>\Phi</math> and <math>B^{\pm}</math> in verbal form.
	* Sweeping clean a tree and <math>{\mathcal A}(\Gamma)\equiv{\mathcal A}(\uparrow_{b_1(\Gamma)})</math>.		* Sweeping clean a tree and <math>{\mathcal A}(\Gamma)\equiv{\mathcal A}(\uparrow_{b_1(\Gamma)})</math>.
	[[Image:06-1350-TRPhiB.png\|center\|500px]]
	* <math>{\mathcal A}(\uparrow_n)</math> is a VS-algebra (see more at [[VS, TS and TG Algebras]]).
	* In the coordinates above, write the <math>TR\Phi B</math> relations in various algebraic notations.
	** R4: <math>(1230)^\star B^\pm\cdot(1213)^\star B^\pm\cdot(1023)^\star\Phi=(1123)^\star\Phi\cdot(1233)^\star B^\pm</math>.
	** <math>B^{\pm}</math> in terms of <math>\Phi</math> and <math>R</math> and <math>R</math> in terms of <math>T</math>.
	** R3, R2, R1
	** Symmetry of <math>\Phi</math> and of <math>B^{\pm}</math>.
	** <math>u</math>, <math>d</math> and <math>\#</math>
	** Idempotence for <math>T</math>, <math>R</math>, <math>\Phi</math> and <math>B^{\pm}</math>.

Drorbn at 13:53, 14 November 2006

2006-11-14T13:53:21Z

← Older revision		Revision as of 09:53, 14 November 2006
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	* Sweeping clean a tree and <math>{\mathcal A}(\Gamma)\equiv{\mathcal A}(\uparrow_{b_1(\Gamma)})</math>.		* Sweeping clean a tree and <math>{\mathcal A}(\Gamma)\equiv{\mathcal A}(\uparrow_{b_1(\Gamma)})</math>.
	[[Image:06-1350-TRPhiB.png\|center\|500px]]		[[Image:06-1350-TRPhiB.png\|center\|500px]]
			* <math>{\mathcal A}(\uparrow_n)</math> is a VS-algebra (see more at [[VS, TS and TG Algebras]]).
	* In the coordinates above, write the <math>TR\Phi B</math> relations in various algebraic notations.		* In the coordinates above, write the <math>TR\Phi B</math> relations in various algebraic notations.
			** R4: <math>(1230)^\star B^\pm\cdot(1213)^\star B^\pm\cdot(1023)^\star\Phi=(1123)^\star\Phi\cdot(1233)^\star B^\pm</math>.
	** R4
	** <math>B^{\pm}</math> in terms of <math>\Phi</math> and <math>R</math> and <math>R</math> in terms of <math>T</math>.		** <math>B^{\pm}</math> in terms of <math>\Phi</math> and <math>R</math> and <math>R</math> in terms of <math>T</math>.
	** R3, R2, R1		** R3, R2, R1

Drorbn at 02:07, 14 November 2006

2006-11-14T02:07:16Z

← Older revision		Revision as of 22:07, 13 November 2006
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	[[Image:06-1350-TRPhiB.png\|center\|500px]]		[[Image:06-1350-TRPhiB.png\|center\|500px]]
	* In the coordinates above, write the <math>TR\Phi B</math> relations in various algebraic notations.		* In the coordinates above, write the <math>TR\Phi B</math> relations in various algebraic notations.
			** R4
			** <math>B^{\pm}</math> in terms of <math>\Phi</math> and <math>R</math> and <math>R</math> in terms of <math>T</math>.
			** R3, R2, R1
			** Symmetry of <math>\Phi</math> and of <math>B^{\pm}</math>.
			** <math>u</math>, <math>d</math> and <math>\#</math>
			** Idempotence for <math>T</math>, <math>R</math>, <math>\Phi</math> and <math>B^{\pm}</math>.

Drorbn at 15:57, 13 November 2006

2006-11-13T15:57:17Z

← Older revision		Revision as of 11:57, 13 November 2006
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	{{In Preparation}}		{{In Preparation}}

			==Today's Agenda==
	Today's handout was taken from [http://www.math.toronto.edu/~drorbn/Talks/HUJI-001116/index.html Talks: HUJI-001116 (Knotted Trivalent Graphs, Tetrahedra and Associators)].

			* Recall planar algebras and the planar algebra of shielded chord diagrams.
			* Finish describing the necessary relations between <math>T</math>, <math>R</math>, <math>\Phi</math> and <math>B^{\pm}</math> in verbal form.
			* Sweeping clean a tree and <math>{\mathcal A}(\Gamma)\equiv{\mathcal A}(\uparrow_{b_1(\Gamma)})</math>.
			[[Image:06-1350-TRPhiB.png\|center\|500px]]
			* In the coordinates above, write the <math>TR\Phi B</math> relations in various algebraic notations.

Drorbn at 14:24, 9 November 2006

2006-11-09T14:24:11Z

← Older revision		Revision as of 10:24, 9 November 2006
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			{{06-1350/Navigation}}

	{{In Preparation}}		{{In Preparation}}

Drorbn at 14:23, 9 November 2006

2006-11-09T14:23:44Z

New page

{{In Preparation}}

Today's handout was taken from [http://www.math.toronto.edu/~drorbn/Talks/HUJI-001116/index.html Talks: HUJI-001116 (Knotted Trivalent Graphs, Tetrahedra and Associators)].