Pentagon Relations in Direct Sums and Grassmann Algebras

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.

References in corpus (7)

• On Discrete 3-Dimensional Equations Associated with the Local Yang-Baxter Relation
• Functional Tetrahedron Equation
• Tetrahedron Equation and Quantum R Matrices for Spin Representations of B^{(1)}_n, D^{(1)}_n and D^{(2)}_{n+1}
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• Quantization of three-wave equations
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Cited by in corpus (6)

• Grassmannian-parameterized solutions to direct-sum polygon and simplex equations
• Heptagon relation in a direct sum
• Parameterizing the Simplest Grassmann-Gaussian Relations for Pachner Move 3-3
• Special 2-cocycles and 3--3 Pachner move relations in Grassmann algebra
• Polynomial-valued constant hexagon cohomology
• Heptagon relations from a simplicial 3-cocycle, and their cohomology