Graded Bundles in the Category of Lie Groupoids
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Graded Bundles in the Category of Lie Groupoids
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| Creator |
Bruce, A.J.
Grabowska, K. Grabowski, J. |
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| 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.
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| Date |
2019-02-13T17:58:32Z
2019-02-13T17:58:32Z 2015 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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