
SIGMA 9 (2013), 030, 16 pages arXiv:1212.4462
https://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 ndimensional 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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