On Associators and the Grothendieck-Teichmuller Group I

Abstract

We present a formalism within which the relationship (discovered by Drinfel'd) 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 re-prove 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.

AMSLaTeX, 25 pages; several improvements and some added details. http://www.ma.huji.ac.il/~drorbn

References in corpus (2)

• The universal Vassiliev-Kontsevich invariant for framed oriented links
• Combinatorial expression for universal Vassiliev link invariant

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• Conjectured enumeration of Vassiliev invariants