07-1352/Class Notes for January 23
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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:
