Pentagon Relations in Direct Sums and Grassmann Algebras

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2013
• Main Authors: Korepanov, I.G., Sadykov, N.M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149234
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Pentagon Relations in Direct Sums and Grassmann Algebras / I.G. Korepanov, N.M. Sadykov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 16 назв. — англ.

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.