On associators and the Grothendieck-Teichmuller group, I |
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Authors: | D. Bar-Natan |
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Affiliation: | (1) Institute of Mathematics, The Hebrew University, Giv'at-Ram, Jerusalem 91904, Israel, e-mail: drorbn@math.huji.ac.il, IL |
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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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Keywords: | . Associator Grothendieck-Teichmuller braids pentagon. |
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