Pentagon Relations in Direct Sums and Grassmann Algebras
  We construct vast families of orthogonal operators obeying pentagon relation in a direct sum of three n-dimensional vector spaces. As a consequence, we obtain pentagon relations in Grassmann algebras, making a far reaching generalization of exotic Reidemeister torsions. 
Igor G. Korepanov and Nurlan M. Sadykov
math-ph math.AT math.MP math.QA