Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908732841000960 |
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| author | Laurent, Adrien Busnot Li, Yunnan Sheng, Yunhe |
| author_facet | Laurent, Adrien Busnot Li, Yunnan Sheng, Yunhe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21971 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration Laurent, Adrien Busnot Li, Yunnan Sheng, Yunhe Rings and Algebras Numerical Analysis Combinatorics 17B38, 16T05, 17B35, 41A58, 65L06 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. |
| title | Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration |
| topic | Rings and Algebras Numerical Analysis Combinatorics 17B38, 16T05, 17B35, 41A58, 65L06 |
| url | https://arxiv.org/abs/2512.21971 |