Geodesic
Post-Lie algebras in Regularity Structures
Forum of Mathematics, Sigma, Tome 11 (2023)

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In this work, we construct the deformed Butcher-Connes-Kreimer Hopf algebra coming from the theory of Regularity Structures as the universal envelope of a post-Lie algebra. We show that this can be done using either of the two combinatorial structures that have been proposed in the context of singular SPDEs: decorated trees and multi-indices. Our construction is inspired from multi-indices where the Hopf algebra was obtained as the universal envelope of a Lie algebra, and it has been proved that one can find a basis that is symmetric with respect to certain elements. We show that this Lie algebra comes from an underlying post-Lie structure. 
@article{10_1017_fms_2023_93,
     author = {Yvain Bruned and Foivos Katsetsiadis},
     title = {Post-Lie algebras in {Regularity} {Structures}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {11},
     year = {2023},
     doi = {10.1017/fms.2023.93},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.93/}
}
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Yvain Bruned; Foivos Katsetsiadis. Post-Lie algebras in Regularity Structures. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.93

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