Reference : Connections adapted to non-negatively graded structure
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Connections adapted to non-negatively graded structure
Bruce, Andrew mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
International Journal of Geometric Methods in Modern Physics
World Scientific
Yes (verified by ORBilu)
[en] Graded Bundles ; Double Vector Bundles ; Connections
[en] Graded bundles are a particularly nice class of graded manifolds and represent a natural generalization of vector bundles. By exploiting the formalism of supermanifolds to describe Lie algebroids, we define the notion of a weighted A-connection on a graded bundle. In a natural sense weighted A-connections are adapted to the basic geometric structure of a graded bundle in the same way as linear A-connections are adapted to the structure of a vector bundle. This notion generalizes directly to multi-graded bundles and in particular we present the notion of a bi-weighted A-connection on a double vector bundle. We prove the existence of such adapted connections and use them to define (quasi-)actions of Lie algebroids on graded bundles.

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