A cellular braid action and the Yang - Baxter equation

Details A cellular braid action and the Yang - Baxter equation A cellular braid action and the Yang - Baxter equation

1996-06-19

arxiv.org/abs/q-alg/9606015v1

Mathematics

Quantum Algebra

8 pages, requires LaTeX2e with AMS extensions

Scientific paper

Using a theorem of Schechtman - Varchenko on integral expressions for solutions of Knizhnik - Zamolodchikov equations we prove that the solutions of the Yang - Baxter equation associated to complex simple Lie algebras belong to the class of generalised Magnus representations of the braid group. Hence they can be obtained from the homology of a certain cell complex, or equivalently as group homology of iterated free groups.

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