Graded Bundles in the Category of Lie Groupoids
We define and make initial study of Lie groupoids equipped with a compatible homogeneity (or graded bundle) structure, such objects we will refer to as weighted Lie groupoids. One can think of weighted Lie groupoids as graded manifolds in the category of Lie groupoids. This is a very rich geometrica...
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| Дата: | 2015 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147161 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Graded Bundles in the Category of Lie Groupoids / A.J. Bruce, K. Grabowska, J. Grabowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 46 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1471612019-02-14T01:25:45Z Graded Bundles in the Category of Lie Groupoids Bruce, A.J. Grabowska, K. Grabowski, J. We define and make initial study of Lie groupoids equipped with a compatible homogeneity (or graded bundle) structure, such objects we will refer to as weighted Lie groupoids. One can think of weighted Lie groupoids as graded manifolds in the category of Lie groupoids. This is a very rich geometrical theory with numerous natural examples. Note that VB-groupoids, extensively studied in the recent literature, form just the particular case of weighted Lie groupoids of degree one. We examine the Lie theory related to weighted groupoids and weighted Lie algebroids, objects defined in a previous publication of the authors, which are graded manifolds in the category of Lie algebroids, showing that they are naturally related via differentiation and integration. In this work we also make an initial study of weighted Poisson-Lie groupoids and weighted Lie bi-algebroids, as well as weighted Courant algebroids. 2015 Article Graded Bundles in the Category of Lie Groupoids / A.J. Bruce, K. Grabowska, J. Grabowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 46 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 22A22; 55R10; 58E40; 58H05 DOI:10.3842/SIGMA.2015.090 http://dspace.nbuv.gov.ua/handle/123456789/147161 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We define and make initial study of Lie groupoids equipped with a compatible homogeneity (or graded bundle) structure, such objects we will refer to as weighted Lie groupoids. One can think of weighted Lie groupoids as graded manifolds in the category of Lie groupoids. This is a very rich geometrical theory with numerous natural examples. Note that VB-groupoids, extensively studied in the recent literature, form just the particular case of weighted Lie groupoids of degree one. We examine the Lie theory related to weighted groupoids and weighted Lie algebroids, objects defined in a previous publication of the authors, which are graded manifolds in the category of Lie algebroids, showing that they are naturally related via differentiation and integration. In this work we also make an initial study of weighted Poisson-Lie groupoids and weighted Lie bi-algebroids, as well as weighted Courant algebroids. |
| format |
Article |
| author |
Bruce, A.J. Grabowska, K. Grabowski, J. |
| spellingShingle |
Bruce, A.J. Grabowska, K. Grabowski, J. Graded Bundles in the Category of Lie Groupoids Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bruce, A.J. Grabowska, K. Grabowski, J. |
| author_sort |
Bruce, A.J. |
| title |
Graded Bundles in the Category of Lie Groupoids |
| title_short |
Graded Bundles in the Category of Lie Groupoids |
| title_full |
Graded Bundles in the Category of Lie Groupoids |
| title_fullStr |
Graded Bundles in the Category of Lie Groupoids |
| title_full_unstemmed |
Graded Bundles in the Category of Lie Groupoids |
| title_sort |
graded bundles in the category of lie groupoids |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147161 |
| citation_txt |
Graded Bundles in the Category of Lie Groupoids / A.J. Bruce, K. Grabowska, J. Grabowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 46 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT bruceaj gradedbundlesinthecategoryofliegroupoids AT grabowskak gradedbundlesinthecategoryofliegroupoids AT grabowskij gradedbundlesinthecategoryofliegroupoids |
| first_indexed |
2023-05-20T17:26:45Z |
| last_indexed |
2023-05-20T17:26:45Z |
| _version_ |
1796153312036257792 |