7 citations · 8 across the 3 of their papers we have counts for
9 papers
Duality and triple structures
Kirill C. H. Mackenzie
We first recall the basic theory of double vector bundles and the canonical pairing of their duals introduced by the author and by Konieczna and Urbanski. We then show that the rel…
On certain canonical diffeomorphisms in symplectic and Poisson geometry
K. C. H. Mackenzie
The canonical involution of a double (=iterated) tangent bundle may be dualized in different ways to yield relations between the Tulczyjew diffeomorphism, the Poisson anchor associ…
Differential operators and actions of Lie algebroids
Y. Kosmann-Schwarzbach, K. C. H. Mackenzie
We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related conc…
Notions of double for Lie algebroids
K. C. H. Mackenzie
We define an abstract notion of double Lie algebroid, which includes as particular cases: (1) the double Lie algebroid of a double Lie groupoid in the sense of the author, such as…
Double Lie algebroids and the double of a Lie bialgebroid
K. C. H. Mackenzie
We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that th…
On symplectic double groupoids and the duality of Poisson groupoids
Kirill C. H. Mackenzie
We prove that the cotangent of a double Lie groupoid S has itself a double groupoid structure with sides the duals of associated Lie algebroids, and double base the dual of the Lie…