Geometric post-Lie deformations of post-Lie algebras and regularity structures Article Swipe

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Julien Jacques ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2508.01560

In order to derive a class of geometric-type deformations of post-Lie algebras, we first extend the geometrical notions of torsion and curvature for a general bilinear operation on a Lie algebra, then we derive compatibility conditions which will ensure that the post-Lie structure remains preserved. This type of deformation applies in particular to the post-Lie algebra introduced in arXiv:2306.02484v3 in the context of regularity structures theory. We use this deformation to derive a pre-Lie structure for the regularity structures approach given in arXiv:2103.04187v4, which is isomorphic to the post-Lie algebra studied in arXiv:2306.02484v3 at the level of their associated Hopf algebras. In the case of sections of smooth vector bundles of a finite-dimensional manifold, this deformed structure contains also, as a subalgebra, the post-Lie algebra structure introduced in arXiv:1203.4738v3 in the geometrical context of moving frames.

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2508.01560
PDF: https://arxiv.org/pdf/2508.01560
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OpenAlex ID: https://openalex.org/W4417099710

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DOI: https://doi.org/10.48550/arxiv.2508.01560

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Title: Geometric post-Lie deformations of post-Lie algebras and regularity structures

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Language: en

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Publication year: 2025

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Publication date: 2025-08-03

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Authors: Julien Jacques

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Landing page: https://arxiv.org/abs/2508.01560

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