Geometric post-Lie deformations of post-Lie algebras and regularity structures
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913972551155712 |
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| author | Jacques, Jean-David |
| author_facet | Jacques, Jean-David |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric post-Lie deformations of post-Lie algebras and regularity structures Jacques, Jean-David Commutative Algebra Analysis of PDEs Differential Geometry Probability Rings and Algebras 60L30, 60L70, 16S30, 16T05, 53A99, 53C05 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. |
| title | Geometric post-Lie deformations of post-Lie algebras and regularity structures |
| topic | Commutative Algebra Analysis of PDEs Differential Geometry Probability Rings and Algebras 60L30, 60L70, 16S30, 16T05, 53A99, 53C05 |
| url | https://arxiv.org/abs/2508.01560 |