Abstract.
We present a formalism within which the relationship (discovered by Drinfel'd in [Dr1], [Dr2]) between associators (for quasi-triangular quasi-Hopf algebras) and (a variant of) the Grothendieck-Teichmuller group becomes simple and natural, leading to a simplification of Drinfel'd's original work. In particular, we reprove that rational associators exist and can be constructed iteratively, though the proof itself still depends on the apriori knowledge that a not-necessarily-rational associator exists.
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Bar-Natan, D. On associators and the Grothendieck-Teichmuller group, I. Sel. math., New ser. 4, 183 (1998). https://doi.org/10.1007/s000290050029
DOI: https://doi.org/10.1007/s000290050029