48 citations · 428 across the 48 of their papers we have counts for
6 papers · 1 filter
Polarisation of Graded Bundles
Andrew James Bruce, Janusz Grabowski, Mikolaj Rotkiewicz
We construct the full linearisation functor which takes a graded bundle of degree (a particular kind of graded manifold) and produces a -fold vector bundle. We fully charact…
New developments in geometric mechanics
A. J. Bruce, K. Grabowska, J. Grabowski +1
We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of thes…
Remarks on Contact and Jacobi Geometry
Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski
We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts ar…
Kirillov structures up to homotopy
Andrew James Bruce, Alfonso G. Tortorella
We present the notion of higher Kirillov brackets on the sections of an even line bundle over a supermanifold. When the line bundle is trivial we shall speak of higher Jacobi brack…
Killing sections and sigma models with Lie algebroid targets
Andrew James Bruce
We define and examine the notion of a Killing section of a Riemannian Lie algebroid as a natural generalisation of a Killing vector field. We show that the various expression for a…
Graded Bundles in the Category of Lie Groupoids
Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski
We define and make initial study of Lie groupoids equipped with a compatible homogeneity (or graded bundle) structure, such objects we will refer to as weighted Lie groupoids. One…