Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms
We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a special kind. In our approach, higher algebroids are vector bundle...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209869 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms / M. Jóźwikowski, M. Rotkiewicz // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 54 назв. — англ. |
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Jóźwikowski M. Rotkiewicz M. 2025-11-28T09:34:27Z 2018 Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms / M. Jóźwikowski, M. Rotkiewicz // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 54 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 58A20; 58A50; 70G65; 58E30; 70H50 arXiv: 1708.03174 https://nasplib.isofts.kiev.ua/handle/123456789/209869 https://doi.org/10.3842/SIGMA.2018.135 We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a special kind. In our approach, higher algebroids are vector bundle comorphisms between graded-linear bundles satisfying natural axioms. We provide natural examples and discuss applications in geometric mechanics. The authors are grateful to the anonymous referees who put a lot of effort into improving the quality and clarity of the manuscript. This research was supported by the Polish National Science Center under the grant DEC-2012/06/A/ST1/00256. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms |
| spellingShingle |
Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms Jóźwikowski M. Rotkiewicz M. |
| title_short |
Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms |
| title_full |
Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms |
| title_fullStr |
Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms |
| title_full_unstemmed |
Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms |
| title_sort |
higher-order analogs of lie algebroids via vector bundle comorphisms |
| author |
Jóźwikowski M. Rotkiewicz M. |
| author_facet |
Jóźwikowski M. Rotkiewicz M. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a special kind. In our approach, higher algebroids are vector bundle comorphisms between graded-linear bundles satisfying natural axioms. We provide natural examples and discuss applications in geometric mechanics.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209869 |
| citation_txt |
Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms / M. Jóźwikowski, M. Rotkiewicz // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 54 назв. — англ. |
| work_keys_str_mv |
AT jozwikowskim higherorderanalogsofliealgebroidsviavectorbundlecomorphisms AT rotkiewiczm higherorderanalogsofliealgebroidsviavectorbundlecomorphisms |
| first_indexed |
2025-12-04T15:12:48Z |
| last_indexed |
2025-12-04T15:12:48Z |
| _version_ |
1850886003045171200 |