Post-Lie algebras in Regularity Structures

Yvain Bruned; Foivos Katsetsiadis

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arXiv · 2208.00514

Post-Lie algebras in Regularity Structures

Yvain Bruned·Foivos Katsetsiadis

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Abstract

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.

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Yvain Bruned, Foivos Katsetsiadis. 2022-07-31. Post-Lie algebras in Regularity Structures. https://arxiv.org/abs/2208.00514

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