On associators and the Grothendieck-Teichmuller group, I

• D. Bar-Natan ^[1]
  1. [1] Hebrew University of Jerusalem

     Hebrew University of Jerusalem

     Israel

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 4, Nº. 2, 1998, págs. 183-212
• Idioma: inglés
• DOI: 10.1007/s000290050029
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• Resumen

  • 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.