Pentagon Relations in Direct Sums and Grassmann Algebras - Korepanov, I.G.; Sadykov, N.M. (Symmetry, Integrability and Geometry: Methods and Applications, 2013)
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.