A cellular braid action and the Yang - Baxter equation
  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. 
Mirko Luedde