07-1352/Class Notes for January 23: Difference between revisions
No edit summary |
No edit summary |
||
| Line 5: | Line 5: | ||
===The Algebra=== |
===The Algebra=== |
||
Let <math>A_n={\mathbb Q}S_n\otimes{\mathbb Q}\langle x_1\ldots x_n\rangle</math> be the vector-space tensor product of the group ring <math>{\mathbb Q}S_n</math> of the permutation group <math>S_n</math> with the completed free associative algebra <math>{\mathbb Q}\langle x_1\ldots x_n\rangle</math> on (non-commuting) generators <math>x_1\ldots x_n</math> (that is, <math>{\mathbb Q}\langle x_1\ldots x_n\rangle</math> is the ring of non-commutative power series in the variables <math>x_1\ldots x_n</math>). We put an algebra structure on <math>A_n</math> as follows: |
|||
===The Equations=== |
===The Equations=== |
||
Revision as of 14:17, 22 January 2007
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||
The information below is preliminary and cannot be trusted! (v)
A HOMFLY Braidor
The Algebra
Let [math]\displaystyle{ A_n={\mathbb Q}S_n\otimes{\mathbb Q}\langle x_1\ldots x_n\rangle }[/math] be the vector-space tensor product of the group ring [math]\displaystyle{ {\mathbb Q}S_n }[/math] of the permutation group [math]\displaystyle{ S_n }[/math] with the completed free associative algebra [math]\displaystyle{ {\mathbb Q}\langle x_1\ldots x_n\rangle }[/math] on (non-commuting) generators [math]\displaystyle{ x_1\ldots x_n }[/math] (that is, [math]\displaystyle{ {\mathbb Q}\langle x_1\ldots x_n\rangle }[/math] is the ring of non-commutative power series in the variables [math]\displaystyle{ x_1\ldots x_n }[/math]). We put an algebra structure on [math]\displaystyle{ A_n }[/math] as follows:
