An operadic approach to substitution in Lie-Butcher series

2021/03/19 by Ludwig Rahm, Rahm, Ludwig · 1 citation
Chemistry · Mathematics · Medicine · #Advanced Topics in Algebra #Cancer Treatment and Pharmacology #Combinatorics (math.CO) #FOS: Mathematics #Numerical Analysis (math.NA) #Rings and Algebras (math.RA) #Synthetic Organic Chemistry Methods

paper · pdf · doi:10.48550/arxiv.2103.10893

openalex publication_date 2021/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 Q. By considering a module over the post-Lie operad, we get a cointeraction between Q and the Hopf algebra H_N that describes composition for Lie-Butcher series. We use this coaction to describe substitution for Lie-Butcher series.

Cited by

• Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration

Related

• Lie-Butcher series, Geometry, Algebra and Computation
• The loop of formal power series with noncommutative coefficients under\n substitution
• Volume preservation of Butcher series methods from the operad viewpoint
• Operads and the Hopf algebras of renormalisation
• Algebraic structures associated to operads