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arXiv · 2512.21971

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

Adrien Busnot Laurent·Yunnan Li·Yunhe Sheng
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Abstract

In this paper, we introduce the notion of post-Hopf algebroids, generalizing the pre-Hopf algebroids introduced in [Bronasco, Laurent, 2025] in the study of exotic aromatic S-series. We construct action post-Hopf algebroids through actions of post-Hopf algebras. We show that the universal enveloping algebra of a post-Lie-Rinehart algebra (post-Lie algebroid) is naturally a post-Hopf algebroid. As a byproduct, we construct the free post-Lie-Rinehart algebra using a magma algebra with a linear map to the derivation Lie algebra of a commutative associative algebra. Applications in geometric numerical integration on manifolds are given.

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BibTeXRIS

Adrien Busnot Laurent, Yunnan Li, Yunhe Sheng. 2025-12-26. Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration. https://doi.org/10.1017/fms.2026.10263

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