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General theory of lie groupoids and lie algebroids
Part I. The General Theory: 1. Lie groupoids: fundamental theory 2. Lie groupoids: algebraic constructions 3. Lie algebroids: fundamental theory 4. Lie algebroids: algebraic constructions Part II.Expand
Lie bialgebroids and Poisson groupoids
Lie bialgebras arise as infinitesimal invariants of Poisson Lie groups. A Lie bialgebra is a Lie algebra g with a Lie algebra structure on the dual g∗ which is compatible with the Lie algebra g in aExpand
Lie Groupoids and Lie Algebroids in Differential Geometry
Introduction 1. The algebra of groupoids 2. Topological groupoids 3. Lie groupoids and Lie algebroids 4. The cohomology of Lie algebroids 5. An obstruction to the integrability of transitive LieExpand
Algebraic constructions in the category of lie algebroids
The aim of this paper is to give the first general and abstract treatment of the algebraic properties of Lie algebroids. The concept of Lie algebroid was introduced in 1967 by Pradines [lS], as theExpand
Double Lie algebroids and second-order geometry, II
We complete the construction of the double Lie algebroid of a double Lie groupoid begun in the first paper of this title. We show that the Lie algebroid structure of an LA--groupoid may be prolongedExpand
Ehresmann doubles and Drinfel'd doubles for Lie algebroids and Lie bialgebroids
Abstract The word ‘double’ was used by Ehresmann to mean ‘an object X in the category of all X’. Double categories, double groupoids and double vector bundles are instances, but the notion of LieExpand
Integration of Lie bialgebroids
Abstract We prove that under certain mild assumptions a Lie bialgebroid integrates to a Poisson groupoid. This includes, in particular, a new proof of the existence of local symplectic groupoids forExpand
On symplectic double groupoids and the duality of Poisson groupoids
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 algebroid of theExpand