On some relations between generalized associators
Abstract
Let Phi be the KZ associator and PsiN 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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