7 citations · 8 across the 3 of their papers we have counts for
5 papers · 1 filter
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…