On a conjecture by Pierre Cartier about a group of associators

  title={On a conjecture by Pierre Cartier about a group of associators},
  author={Vincel Hoang Ngoc Minh},
In [8], Pierre Cartier conjectured that for any non commutative formal power series Φ on X = {x0, x1} with coefficients in a Q-extension, A, subjected to some suitable conditions, there exists an unique algebra homomorphism φ from the Q-algebra generated by the convergent polyzêtas to A such that Φ is computed from ΦKZ Drinfel’d associator by applying φ to each coefficient. We prove φ exists and it is a free Lie exponential over X. Moreover, we give a complete description of the kernel of polyz… CONTINUE READING
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