Polarisation of Graded Bundles
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Polarisation of Graded Bundles
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| Creator |
Bruce, A.J.
Grabowski, J. Rotkiewicz, M. |
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| 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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| Date |
2019-02-18T14:53:04Z
2019-02-18T14:53:04Z 2016 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/148538 |
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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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