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dc.contributor.author Bruce, A.J.
dc.contributor.author Grabowski, J.
dc.contributor.author Rotkiewicz, M.
dc.date.accessioned 2019-02-18T14:53:04Z
dc.date.available 2019-02-18T14:53:04Z
dc.date.issued 2016
dc.identifier.citation 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. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 55R10; 58A32; 58A50
dc.identifier.other DOI:10.3842/SIGMA.2016.106
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/148538
dc.description.abstract 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. uk_UA
dc.description.sponsorship 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. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Polarisation of Graded Bundles uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA

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