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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148538 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862531076531945472 |
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| author | Bruce, A.J. Grabowski, J. Rotkiewicz, M. |
| author_facet | Bruce, A.J. Grabowski, J. Rotkiewicz, M. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-24T04:39:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148538 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T04:39:51Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
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| spelling | Bruce, A.J. Grabowski, J. Rotkiewicz, M. 2019-02-18T14:53:04Z 2019-02-18T14:53:04Z 2016 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 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Polarisation of Graded Bundles Article published earlier |
| spellingShingle | Polarisation of Graded Bundles Bruce, A.J. Grabowski, J. Rotkiewicz, M. |
| title | Polarisation of Graded Bundles |
| title_full | Polarisation of Graded Bundles |
| title_fullStr | Polarisation of Graded Bundles |
| title_full_unstemmed | Polarisation of Graded Bundles |
| title_short | Polarisation of Graded Bundles |
| title_sort | polarisation of graded bundles |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148538 |
| work_keys_str_mv | AT bruceaj polarisationofgradedbundles AT grabowskij polarisationofgradedbundles AT rotkiewiczm polarisationofgradedbundles |