Duality for Graded Manifolds

We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belong to a different category than the initial ones, namely graded polynomial (co)alg...

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Bibliographic Details
Published in:Reports on mathematical physics 2017-08, Vol.80 (1), p.115-142
Main Authors: Grabowski, Janusz, Jóźwikowski, Michał, Rotkiewicz, Mikołaj
Format: Article
Language:English
Subjects:
duality
graded bundle
homogeneity structure
N-manifold
Zakrzewski morphism
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Summary:We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belong to a different category than the initial ones, namely graded polynomial (co)algebra bundles and free graded Weil (co)algebra bundles. Our results are then applied to obtain elegant characterizations of double vector bundles and graded bundles of degree 2. All these results have their supergeometric counterparts. For instance, we give a simple proof of a nice characterisation of N-manifolds of degree 2, announced in the literature.
ISSN:0034-4877
1879-0674
DOI:10.1016/S0034-4877(17)30064-2