06-1350/Class Notes for Tuesday November 14: Difference between revisions

Revision as of 08:53, 14 November 2006

#	Week of...	Links
1	Sep 11	About, Tue, Thu
2	Sep 18	Tue, Kurlin(P), Thu
3	Sep 25	Tue, Photo, Thu
4	Oct 2	HW1, Tue, Thu
5	Oct 9	Tue(P), Thu(P)
6	Oct 16	HW2, Tue(P), Thu(P)
7	Oct 23	Tue(P), Thu
8	Oct 30	HW3, Tue, Thu
9	Nov 6	Tue ( $\nu$ ), Thu
10	Nov 13	Tue, Thu
11	Nov 20	HW4(P), Thu
12	Nov 27	Thu
13	Dec 4	Syzygies in Asymptote, Final
	Jan 8	Grades
Note. (P) means "contains a problem that Dror cares about".
Add your name / see who's in!
On to 07-1352

In Preparation

The information below is preliminary and cannot be trusted! (v)

Recall planar algebras and the planar algebra of shielded chord diagrams.
Finish describing the necessary relations between $T$ , $R$ , $\Phi$ and $B^{\pm }$ in verbal form.
Sweeping clean a tree and ${\mathcal {A}}(\Gamma )\equiv {\mathcal {A}}(\uparrow _{b_{1}(\Gamma )})$ .

${\mathcal {A}}(\uparrow _{n})$ is a VS-algebra (see more at VS, TS and TG Algebras).
In the coordinates above, write the $TR\Phi B$ $TR\Phi B$ relations in various algebraic notations.
- R4: $(1230)^{\star }B^{\pm }\cdot (1213)^{\star }B^{\pm }\cdot (1023)^{\star }\Phi =(1123)^{\star }\Phi \cdot (1233)^{\star }B^{\pm }$ .
- $B^{\pm }$ in terms of $\Phi$ and $R$ and $R$ in terms of $T$ .
- R3, R2, R1
- Symmetry of $\Phi$ and of $B^{\pm }$ .
- $u$ , $d$ and $\#$
- Idempotence for $T$ , $R$ , $\Phi$ and $B^{\pm }$ .

@@ Line 9: / Line 9: @@
 * 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>.
-** 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