Almost Lie Algebroids and Characteristic Classes
Almost Lie algebroids are generalizations of Lie algebroids, when the Jacobiator is not necessarily null. A simple example is given, for which a Lie algebroid bracket or a Courant bundle is not possible for the given anchor, but a natural extension of the bundle and the new anchor allows a Lie algeb...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210054 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Almost Lie Algebroids and Characteristic Classes / M. Popescu, P. Popescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862619499763597312 |
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| author | Popescu, M. Popescu, P. |
| author_facet | Popescu, M. Popescu, P. |
| citation_txt | Almost Lie Algebroids and Characteristic Classes / M. Popescu, P. Popescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Almost Lie algebroids are generalizations of Lie algebroids, when the Jacobiator is not necessarily null. A simple example is given, for which a Lie algebroid bracket or a Courant bundle is not possible for the given anchor, but a natural extension of the bundle and the new anchor allows a Lie algebroid bracket. A cohomology and related characteristic classes of an almost Lie algebroid are also constructed. We prove that these characteristic classes are all pull-backs of the characteristic classes of the base space, as in the case of a Lie algebroid.
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| first_indexed | 2025-12-07T21:24:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210054 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:13Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Popescu, M. Popescu, P. 2025-12-02T09:29:34Z 2019 Almost Lie Algebroids and Characteristic Classes / M. Popescu, P. Popescu // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D17; 53C05; 58A99 arXiv: 1808.03116 https://nasplib.isofts.kiev.ua/handle/123456789/210054 https://doi.org/10.3842/SIGMA.2019.021 Almost Lie algebroids are generalizations of Lie algebroids, when the Jacobiator is not necessarily null. A simple example is given, for which a Lie algebroid bracket or a Courant bundle is not possible for the given anchor, but a natural extension of the bundle and the new anchor allows a Lie algebroid bracket. A cohomology and related characteristic classes of an almost Lie algebroid are also constructed. We prove that these characteristic classes are all pull-backs of the characteristic classes of the base space, as in the case of a Lie algebroid. The authors thank all three distinct referees for their valuable comments that helped us to improve the content of the paper. The research was supported by the Horizon 2020-2017-RISE777911 project. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Almost Lie Algebroids and Characteristic Classes Article published earlier |
| spellingShingle | Almost Lie Algebroids and Characteristic Classes Popescu, M. Popescu, P. |
| title | Almost Lie Algebroids and Characteristic Classes |
| title_full | Almost Lie Algebroids and Characteristic Classes |
| title_fullStr | Almost Lie Algebroids and Characteristic Classes |
| title_full_unstemmed | Almost Lie Algebroids and Characteristic Classes |
| title_short | Almost Lie Algebroids and Characteristic Classes |
| title_sort | almost lie algebroids and characteristic classes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210054 |
| work_keys_str_mv | AT popescum almostliealgebroidsandcharacteristicclasses AT popescup almostliealgebroidsandcharacteristicclasses |