A comodule-bialgebra structure for word-series substitution and mould composition
arXiv:1609.03549 · doi:10.1016/j.jalgebra.2017.07.002
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.
arXiv commentrevised version, accepted for publication in Journal of Algebra
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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