101 citations · 224 across the 8 of their papers we have counts for
8 papers
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…
Duality functors for -fold vector bundles
Alfonso Gracia-Saz, K. C. H. Mackenzie
Double vector bundles may be dualized in two distinct ways and these duals are themselves dual. These two dualizations generate a group, denoted , which i…
VB-groupoids and representation theory of Lie groupoids
Alfonso Gracia-Saz, Rajan Amit Mehta
A VB-groupoid is a Lie groupoid equipped with a compatible linear structure. In this paper, we describe a correspondence, up to isomorphism, between VB-groupoids and 2-term represe…
Duality functors for triple vector bundles
Alfonso Gracia-Saz, Kirill C. H. Mackenzie
We calculate the group of dualization operations for triple vector bundles, showing that it has order 96 and not 72 as given in Mackenzie's original treatment. The group is a nonsp…
Lie algebroid structures on double vector bundles and representation theory of Lie algebroids
Alfonso Gracia-Saz, Rajan Amit Mehta
A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie a…
Multidimensional quantum normal forms, Moyal star product, and torus quantization
Matthew Cargo, Alfonso Gracia-Saz, R G Littlejohn
A normal form transformation is carried out on the operators of a complete set of commuting observables in a multidimensional, integrable quantum system, mapping them by unitary co…