An operadic approach to substitution in Lie–Butcher series
Forum of Mathematics, Sigma, Tome 10 (2022)
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The paper follows an operadic approach to provide a bialgebraic description of substitution for Lie–Butcher series. We first show how the well-known bialgebraic description for substitution in Butcher’s B-series can be obtained from the pre-Lie operad. We then apply the same construction to the post-Lie operad to arrive at a bialgebra $\mathcal {Q}$. By considering a module over the post-Lie operad, we get a cointeraction between $\mathcal {Q}$ and the Hopf algebra $\mathcal {H}_{N}$ that describes composition for Lie–Butcher series. We use this coaction to describe substitution for Lie–Butcher series.
@article{10_1017_fms_2022_12,
author = {Ludwig Rahm},
title = {An operadic approach to substitution in {Lie{\textendash}Butcher} series},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {10},
year = {2022},
doi = {10.1017/fms.2022.12},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.12/}
}
Ludwig Rahm. An operadic approach to substitution in Lie–Butcher series. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.12
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