07-1352/Class Notes for January 23: Difference between revisions
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===The Algebra=== |
===The Algebra=== |
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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: |
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===The Equations=== |
===The Equations=== |
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Revision as of 14:17, 22 January 2007
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In Preparation
The information below is preliminary and cannot be trusted! (v)
A HOMFLY Braidor
The Algebra
Let be the vector-space tensor product of the group ring of the permutation group with the completed free associative algebra on (non-commuting) generators (that is, is the ring of non-commutative power series in the variables ). We put an algebra structure on as follows:
