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This article is cited in 6 scientific papers (total in 6 papers)
Polarisation of Graded Bundles
Andrew James Brucea, Janusz Grabowskia, Mikołaj Rotkiewiczb a Institute of Mathematics, Polish Academy of Sciences, Poland
b Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland
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 ${\mathbb S}_k$. 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.
Keywords:
graded manifolds; $N$-manifolds; $k$-fold vector bundles; polarisation; supermanifolds.
Received: December 14, 2015; in final form October 25, 2016; Published online November 2, 2016
Citation:
Andrew James Bruce, Janusz Grabowski, Mikołaj Rotkiewicz, “Polarisation of Graded Bundles”, SIGMA, 12 (2016), 106, 30 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1188 https://www.mathnet.ru/eng/sigma/v12/p106
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