Local Rigidity of Quasi--Lie Brackets on Quaternionic Banach Modules and Applications to Nonlinear PDEs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911204017963008 |
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| author | Athmouni, Nassim |
| author_facet | Athmouni, Nassim |
| contents | We establish a local rigidity theorem for quasi--Lie brackets on quaternionic Banach right modules. Under quantitative control of antisymmetry and Jacobi defects, we construct an explicit bilinear correction that preserves right $\mathbb{H}$--linearity and restores the exact Lie property. The approach combines a radial homotopy operator, a controlled Neumann-series inversion, and a finite-rank adjustment, all with explicit operator estimates. This constructive framework bridges quaternionic functional analysis with rigidity theory and yields concrete applications to nonlinear PDEs, including local well-posedness and Beale--Kato--Majda continuation criteria with explicit thresholds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_10124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local Rigidity of Quasi--Lie Brackets on Quaternionic Banach Modules and Applications to Nonlinear PDEs Athmouni, Nassim Rings and Algebras Analysis of PDEs Functional Analysis 17B66, 46G20, 47A10, 35Q35 I.1.2; G.1.10; I.1.1 We establish a local rigidity theorem for quasi--Lie brackets on quaternionic Banach right modules. Under quantitative control of antisymmetry and Jacobi defects, we construct an explicit bilinear correction that preserves right $\mathbb{H}$--linearity and restores the exact Lie property. The approach combines a radial homotopy operator, a controlled Neumann-series inversion, and a finite-rank adjustment, all with explicit operator estimates. This constructive framework bridges quaternionic functional analysis with rigidity theory and yields concrete applications to nonlinear PDEs, including local well-posedness and Beale--Kato--Majda continuation criteria with explicit thresholds. |
| title | Local Rigidity of Quasi--Lie Brackets on Quaternionic Banach Modules and Applications to Nonlinear PDEs |
| topic | Rings and Algebras Analysis of PDEs Functional Analysis 17B66, 46G20, 47A10, 35Q35 I.1.2; G.1.10; I.1.1 |
| url | https://arxiv.org/abs/2510.10124 |