Real involutive systems on compact Lie groups
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914350894153728 |
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| author | Araújo, Gabriel Ferra, Igor A. Jahnke, Max R. Ragognette, Luis F. |
| author_facet | Araújo, Gabriel Ferra, Igor A. Jahnke, Max R. Ragognette, Luis F. |
| contents | On a compact connected Lie group $G$, we study the global solvability and the cohomology spaces of the differential complex associated with an essentially real involutive structure that is invariant under left translations. We prove that solvability in the first degree of the complex implies solvability in all other degrees, and furnish a converse for this fact under a certain commutativity hypothesis (that always holds when $G$ is a torus). Additionally, it is proved that the solvability holds when the structure comes from the Lie algebra of a closed subgroup of $G$. We also investigate real tube structures when $G$ is the base manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22210 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Real involutive systems on compact Lie groups Araújo, Gabriel Ferra, Igor A. Jahnke, Max R. Ragognette, Luis F. Analysis of PDEs 35F35 (primary), 58J10, 35R03 (secondary) On a compact connected Lie group $G$, we study the global solvability and the cohomology spaces of the differential complex associated with an essentially real involutive structure that is invariant under left translations. We prove that solvability in the first degree of the complex implies solvability in all other degrees, and furnish a converse for this fact under a certain commutativity hypothesis (that always holds when $G$ is a torus). Additionally, it is proved that the solvability holds when the structure comes from the Lie algebra of a closed subgroup of $G$. We also investigate real tube structures when $G$ is the base manifold. |
| title | Real involutive systems on compact Lie groups |
| topic | Analysis of PDEs 35F35 (primary), 58J10, 35R03 (secondary) |
| url | https://arxiv.org/abs/2602.22210 |