On some relations between generalized associators

2006/09/15 by Benjamin Enriquez, Enriquez, B.
Chemistry · Mathematics · Physics and Astronomy · #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.math/0609440

openalex publication_date 2006/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Phi be the KZ associator and Psi_N be its analogue for N-th roots of 1. We prove a hexagon relation for Psi₄. Similarly to the Broadhurst (for Psi₂) and Okuda (for Psi₄) duality relations, it relies on the "supplementary" (i.e., non-dihedral) symmetries of C^* - mu₄(C) (i.e., the octahedron group S₄). We also derive relations between Phi and Psi₂, which are analogues of equations, found by Nakamura and Schneps, satisfied by the image of the Galois group of Q in the Grothendieck-Teichm"uller group.

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