On Complex Lie Algebroids with Constant Real Rank
We associate a real distribution to any complex Lie algebroid that we call the distribution of real elements and a new invariant that we call real rank, given by the pointwise rank of this distribution. When the real rank is constant, we obtain a real Lie algebroid inside the original complex Lie al...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/213532 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Complex Lie Algebroids with Constant Real Rank. Dan Aguero. SIGMA 21 (2025), 044, 25 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862582504864612352 |
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| author | Aguero, Dan |
| author_facet | Aguero, Dan |
| citation_txt | On Complex Lie Algebroids with Constant Real Rank. Dan Aguero. SIGMA 21 (2025), 044, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We associate a real distribution to any complex Lie algebroid that we call the distribution of real elements and a new invariant that we call real rank, given by the pointwise rank of this distribution. When the real rank is constant, we obtain a real Lie algebroid inside the original complex Lie algebroid. Under another regularity condition, we associate a complex Lie subalgebroid that we call the minimal complex subalgebroid. We also provide a local splitting for complex Lie algebroids with constant real rank. In the last part, we introduce the complex matched pair of skew-algebroids; these pairs produce complex Lie algebroid structures on the complexification of a vector bundle. We use this operation to characterize all the complex Lie algebroid structures on the complexification of real vector bundles.
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| first_indexed | 2026-03-21T12:06:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213532 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T12:06:27Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Aguero, Dan 2026-02-18T11:26:43Z 2025 On Complex Lie Algebroids with Constant Real Rank. Dan Aguero. SIGMA 21 (2025), 044, 25 pages 1815-0659 2020 Mathematics Subject Classification: 53D20 arXiv:2401.05274 https://nasplib.isofts.kiev.ua/handle/123456789/213532 https://doi.org/10.3842/SIGMA.2025.044 We associate a real distribution to any complex Lie algebroid that we call the distribution of real elements and a new invariant that we call real rank, given by the pointwise rank of this distribution. When the real rank is constant, we obtain a real Lie algebroid inside the original complex Lie algebroid. Under another regularity condition, we associate a complex Lie subalgebroid that we call the minimal complex subalgebroid. We also provide a local splitting for complex Lie algebroids with constant real rank. In the last part, we introduce the complex matched pair of skew-algebroids; these pairs produce complex Lie algebroid structures on the complexification of a vector bundle. We use this operation to characterize all the complex Lie algebroid structures on the complexification of real vector bundles. The author acknowledges Henrique Bursztyn for proposing the topic and his many valuable observations. The author is also grateful to Hudson Lima, Roberto Rubio, and Pedro Frejlich for many fruitful and helpful conversations. We are also thankful to the anonymous referees for their valuable comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Complex Lie Algebroids with Constant Real Rank Article published earlier |
| spellingShingle | On Complex Lie Algebroids with Constant Real Rank Aguero, Dan |
| title | On Complex Lie Algebroids with Constant Real Rank |
| title_full | On Complex Lie Algebroids with Constant Real Rank |
| title_fullStr | On Complex Lie Algebroids with Constant Real Rank |
| title_full_unstemmed | On Complex Lie Algebroids with Constant Real Rank |
| title_short | On Complex Lie Algebroids with Constant Real Rank |
| title_sort | on complex lie algebroids with constant real rank |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213532 |
| work_keys_str_mv | AT aguerodan oncomplexliealgebroidswithconstantrealrank |