Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 9 (2013), 030, 16 pages      arXiv:1212.4462      http://dx.doi.org/10.3842/SIGMA.2013.030

Pentagon Relations in Direct Sums and Grassmann Algebras

Igor G. Korepanov and Nurlan M. Sadykov
Moscow State University of Instrument Engineering and Computer Sciences, 20 Stromynka Str., Moscow 107996, Russia

Received December 19, 2012, in final form April 05, 2013; Published online April 10, 2013

Abstract
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.

Key words: Pachner moves; pentagon relations; Grassmann algebras.

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