On the Drinfeld generators of $\mathfrak{grt}_1({\bf k})$ and $\Gamma$-functions for associators

We prove that the Drinfeld generators of $\mathfrak{grt}_1({\bf k})$ linearly span the image of this Lie algebra in the abelianization of the commutator of the free Lie algebra with two generators. We show that this result implies $\Gamma$-function formulas for arbitrary associators.

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Published 1 January 2006