Polarisation of Graded Bundles
We construct the full linearisation functor which takes a graded bundle of degree k (a particular kind of graded manifold) and produces a k-fold vector bundle. We fully characterise the image of the full linearisation functor and show that we obtain a subcategory of k-fold vector bundles consisting...
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| Date: | 2016 |
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Інститут математики НАН України
2016
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Cite this: | Polarisation of Graded Bundles / A.J. Bruce, J. Grabowski, M. Rotkiewicz // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 38 назв. — англ. |
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oai:nasplib.isofts.kiev.ua:123456789-1485382025-02-23T17:34:19Z Polarisation of Graded Bundles Bruce, A.J. Grabowski, J. Rotkiewicz, M. We construct the full linearisation functor which takes a graded bundle of degree k (a particular kind of graded manifold) and produces a k-fold vector bundle. We fully characterise the image of the full linearisation functor and show that we obtain a subcategory of k-fold vector bundles consisting of symmetric k-fold vector bundles equipped with a family of morphisms indexed by the symmetric group Sk. Interestingly, for the degree 2 case this additional structure gives rise to the notion of a symplectical double vector bundle, which is the skew-symmetric analogue of a metric double vector bundle. We also discuss the related case of fully linearising N-manifolds, and how one can use the full linearisation functor to ''superise'' a graded bundle. The authors thank the anonymous referees whose comments and suggestions have served to improve the presentation of this work. Research funded by the Polish National Science Centre grant under the contract number DEC-2012/06/A/ST1/00256. 2016 Article Polarisation of Graded Bundles / A.J. Bruce, J. Grabowski, M. Rotkiewicz // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 38 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 55R10; 58A32; 58A50 DOI:10.3842/SIGMA.2016.106 https://nasplib.isofts.kiev.ua/handle/123456789/148538 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
We construct the full linearisation functor which takes a graded bundle of degree k (a particular kind of graded manifold) and produces a k-fold vector bundle. We fully characterise the image of the full linearisation functor and show that we obtain a subcategory of k-fold vector bundles consisting of symmetric k-fold vector bundles equipped with a family of morphisms indexed by the symmetric group Sk. Interestingly, for the degree 2 case this additional structure gives rise to the notion of a symplectical double vector bundle, which is the skew-symmetric analogue of a metric double vector bundle. We also discuss the related case of fully linearising N-manifolds, and how one can use the full linearisation functor to ''superise'' a graded bundle. |
| format |
Article |
| author |
Bruce, A.J. Grabowski, J. Rotkiewicz, M. |
| spellingShingle |
Bruce, A.J. Grabowski, J. Rotkiewicz, M. Polarisation of Graded Bundles Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bruce, A.J. Grabowski, J. Rotkiewicz, M. |
| author_sort |
Bruce, A.J. |
| title |
Polarisation of Graded Bundles |
| title_short |
Polarisation of Graded Bundles |
| title_full |
Polarisation of Graded Bundles |
| title_fullStr |
Polarisation of Graded Bundles |
| title_full_unstemmed |
Polarisation of Graded Bundles |
| title_sort |
polarisation of graded bundles |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| citation_txt |
Polarisation of Graded Bundles / A.J. Bruce, J. Grabowski, M. Rotkiewicz // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 38 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT bruceaj polarisationofgradedbundles AT grabowskij polarisationofgradedbundles AT rotkiewiczm polarisationofgradedbundles |
| first_indexed |
2025-07-22T04:20:44Z |
| last_indexed |
2025-07-22T04:20:44Z |
| _version_ |
1838319450369032192 |