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arXiv · 0910.1932

On a conjecture by Pierre Cartier about a group of associators

Vincel Hoang Ngoc Minh
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Abstract

In \cite{cartier2}, Pierre Cartier conjectured that for any non commutative formal power series $Φ$ on $X=\{x_0,x_1\}$ 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 $Φ_{KZ}$ 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 polyzêta and draw some consequences about a structure of the algebra of convergent polyzêtas and about the arithmetical nature of the Euler constant.

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Vincel Hoang Ngoc Minh. 2012-06-09. On a conjecture by Pierre Cartier about a group of associators. https://arxiv.org/abs/0910.1932

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