35 citations · 105 across the 16 of their papers we have counts for
18 papers
Transitive double Lie algebroids via core diagrams
Madeleine Jotz Lean, Kirill Mackenzie
The core diagram of a double Lie algebroid consists in the core of the double Lie algebroid, together with the two core-anchor maps to the sides of the double Lie algebroid. If the…
Warps and duality for double vector bundles
Magdalini K. Flari, Kirill Mackenzie
A linear section of a double vector bundle is a parallel pair of sections which form a vector bundle morphism; examples include the complete lifts of vector fields to tangent bundl…
Warps and grids for double and triple vector bundles
Magdalini K. Flari, Kirill Mackenzie
A triple vector bundle is a cube of vector bundle structures which commute in the (strict) categorical sense. A grid in a triple vector bundle is a collection of sections of each b…
Poisson Geometry Related to Atiyah Sequences
Kirill Mackenzie, Anatol Odzijewicz, Aneta Sliżewska
We construct and investigate a short exact sequence of Poisson -groupoids which is canonically related to the Atiyah sequence of a -principal bundle . Our resul…
From symplectic groupoids to double structures
Kirill Mackenzie
These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account o…
Double Lie algebroids and representations up to homotopy
Alfonso Gracia-Saz, Madeleine Jotz Lean, Kirill C. H. Mackenzie +1
We show that double Lie algebroids, together with a chosen linear splitting, are equivalent to pairs of 2-term representations up to homotopy satisfying compatibility conditions wh…