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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2018 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2018
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| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862564727007215616 |
|---|---|
| author | Jóźwikowski M. Rotkiewicz M. |
| author_facet | Jóźwikowski M. Rotkiewicz M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-04T15:12:48Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209869 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-04T15:12:48Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms Jóźwikowski M. Rotkiewicz M. |
| title | 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_short | Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms |
| title_sort | higher-order analogs of lie algebroids via vector bundle comorphisms |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209869 |
| work_keys_str_mv | AT jozwikowskim higherorderanalogsofliealgebroidsviavectorbundlecomorphisms AT rotkiewiczm higherorderanalogsofliealgebroidsviavectorbundlecomorphisms |