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...
Saved in:
| Date: | 2016 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2016
|
| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
|---|