TY  - JOUR
A1  - Jotz Lean, Madeleine
A1  - Mackenzie, Kirill C. H.
T1  - Transitive double Lie algebroids via core diagrams
JF  - Journal of Geometric Mechanics
N2  - The core diagram of a double Lie algebroid consists of the core of the double Lie algebroid, together with the two core-anchor maps to the sides of the double Lie algebroid. If these two core-anchors are surjective, then the double Lie algebroid and its core diagram are called transitive. This paper establishes an equivalence between transitive double Lie algebroids, and transitive core diagrams over a fixed base manifold. In other words, it proves that a transitive double Lie algebroid is completely determined by its core diagram.
The comma double Lie algebroid associated to a morphism of Lie algebroids is defined. If the latter morphism is one of the core-anchors of a transitive core diagram, then the comma double algebroid can be quotiented out by the second core-anchor, yielding a transitive double Lie algebroid, which is the one that is equivalent to the transitive core diagram.
Brown's and Mackenzie's equivalence of transitive core diagrams (of Lie groupoids) with transitive double Lie groupoids is then used in order to show that a transitive double Lie algebroid with integrable sides and core is automatically integrable to a transitive double Lie groupoid.
KW  - double Lie algebroids
KW  - double Lie groupoids
KW  - comma category
KW  - representations up to homotopy
KW  - matched pairs
KW  - Lie bialgebroids
KW  - infinitesimal ideal systems
KW  - integration
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-363224
VL  - 13
ER  -