This article is cited in 4 papers

Pentagon Relations in Direct Sums and Grassmann Algebras

Igor G. Korepanov, Nurlan M. Sadykov

Moscow State University of Instrument Engineering and Computer Sciences, 20 Stromynka Str., Moscow 107996, Russia

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.

Keywords: Pachner moves; pentagon relations; Grassmann algebras.

MSC: 15A75; 57Q99; 57R56

Received: December 19, 2012; in final form April 5, 2013; Published online April 10, 2013

Language: English

DOI: 10.3842/SIGMA.2013.030

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ArXiv: 1212.4462