Partial Dirac structures in infinite dimension
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929508310843392 |
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| author | Pelletier, Fernand Cabau, Patrick |
| author_facet | Pelletier, Fernand Cabau, Patrick |
| contents | In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those structures whose classical geometrical results in finite dimension can be extended to this infinite dimensional context. Finally, we are interested in the projective and direct limits of such structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial Dirac structures in infinite dimension Pelletier, Fernand Cabau, Patrick Differential Geometry 46T05, 22E65, 55R10, 70G45 In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those structures whose classical geometrical results in finite dimension can be extended to this infinite dimensional context. Finally, we are interested in the projective and direct limits of such structures. |
| title | Partial Dirac structures in infinite dimension |
| topic | Differential Geometry 46T05, 22E65, 55R10, 70G45 |
| url | https://arxiv.org/abs/2409.13497 |