A comodule-bialgebra structure for word-series substitution and mould composition

Abstract

An internal coproduct is described, which is compatible with Hoffman's quasi-shuffle product. Hoffman's quasi-shuffle Hopf algebra, with deconcatenation coproduct, is a comodule-Hopf algebra over the bialgebra thus defined. The relation with J. Ecalle's mould calculus, i.e. mould composition and contracting arborification, is precised.

revised version, accepted for publication in Journal of Algebra

References in corpus (2)

• Word series for dynamical systems and their numerical integrators
• The Heisenberg product: from Hopf algebras and species to symmetric functions

Cited by in corpus (6)

• Planarly branched rough paths and rough differential equations on homogeneous spaces
• Quasi-shuffle algebras and renormalisation of rough differential equations
• Tropical time series, iterated-sums signatures and quasisymmetric functions
• Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations
• The incidence comodule bialgebra of the Baez-Dolan construction
• Double shuffle relations for arborified zeta values