2025/08/03 by Jacques, Jean-David
Mathematics · Physics and Astronomy · #16S30 #16T05 #53A99 #53C05 #60L30 #60L70 #Advanced Differential Geometry Research #Advanced Topics in Algebra #Analysis of PDEs (math.AP) #Commutative Algebra (math.AC) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Probability (math.PR) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2508.01560
openalex publication_date 2025/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.