06-1350/Class Notes for Tuesday November 14: Difference between revisions
From Drorbn
Jump to navigationJump to search
No edit summary |
No edit summary |
||
| Line 10: | Line 10: | ||
[[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>. |
|||
Revision as of 21:07, 13 November 2006
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||
In Preparation
The information below is preliminary and cannot be trusted! (v)
Today's Agenda
- Recall planar algebras and the planar algebra of shielded chord diagrams.
- Finish describing the necessary relations between [math]\displaystyle{ T }[/math], [math]\displaystyle{ R }[/math], [math]\displaystyle{ \Phi }[/math] and [math]\displaystyle{ B^{\pm} }[/math] in verbal form.
- Sweeping clean a tree and [math]\displaystyle{ {\mathcal A}(\Gamma)\equiv{\mathcal A}(\uparrow_{b_1(\Gamma)}) }[/math].
- In the coordinates above, write the [math]\displaystyle{ TR\Phi B }[/math] relations in various algebraic notations.
- R4
- [math]\displaystyle{ B^{\pm} }[/math] in terms of [math]\displaystyle{ \Phi }[/math] and [math]\displaystyle{ R }[/math] and [math]\displaystyle{ R }[/math] in terms of [math]\displaystyle{ T }[/math].
- R3, R2, R1
- Symmetry of [math]\displaystyle{ \Phi }[/math] and of [math]\displaystyle{ B^{\pm} }[/math].
- [math]\displaystyle{ u }[/math], [math]\displaystyle{ d }[/math] and [math]\displaystyle{ \# }[/math]
- Idempotence for [math]\displaystyle{ T }[/math], [math]\displaystyle{ R }[/math], [math]\displaystyle{ \Phi }[/math] and [math]\displaystyle{ B^{\pm} }[/math].
