Associators in mould theory

2023/12/24 by Furusho, Hidekazu, Hirose, Minoru, Komiyama, Nao
#FOS: Mathematics #Number Theory (math.NT) #Primary 16T05 #Quantum Algebra (math.QA) #Secondary 11M32

paper · doi:10.48550/arxiv.2312.15423

Abstract

By developing various techniques of mould theory, we introduce GARI(\mathscrF)_as+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 GARI(\mathscrF)_as+bal is embedded to Ecalle's set GARI(\mathscrF)_as\astis which is a mould theoretic version of Racinet's double shuffle set.

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