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arXiv · 2312.15423

Associators in mould theory

Hidekazu Furusho·Minoru Hirose·Nao Komiyama
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Abstract

By developing various techniques of mould theory and establishing a quasi-involutive reformulation of Drinfeld's associator set, we introduce $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal}}$, a mould theoretic formulation of Drinfeld's associator set. We give a mould-theoretical generalization of the result that associator relations imply double shuffle relations, namely, we explain that $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal}}$ is embedded into Ecalle's set $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}\ast\mathsf{is}}$ which is a mould theoretic version of Racinet's double shuffle set.

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Hidekazu Furusho, Minoru Hirose, Nao Komiyama. 2023-12-24. Associators in mould theory. https://arxiv.org/abs/2312.15423

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