Vector bundles over Lie groupoids and algebroids
arXiv:1410.5135 · doi:10.1016/j.aim.2015.11.044
Abstract
We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their relation via differentiation and integration. We also show how to extend our techniques to describe the more general Lie theory underlying double Lie algebroids and LA-groupoids.
37 pages
References in corpus (8)
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- Lie algebroid structures on double vector bundles and representation theory of Lie algebroids
- Lie Groupoids and Differentiable Stacks
- VB-groupoids and representation theory of Lie groupoids
- Double Lie algebroids and the double of a Lie bialgebroid
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Cited by in corpus (31)
- VB-groupoids and representation theory of Lie groupoids
- Lie theory of multiplicative tensors
- Remarks on Contact and Jacobi Geometry
- Linear duals of graded bundles and higher analogues of (Lie) algebroids
- Riemannian metrics on differentiable stacks
- Van Est isomorphism for homogeneous cochains
- Morita equivalences of vector bundles
- Holomorphic Jacobi Manifolds and Holomorphic Contact Groupoids
- Differential forms with values in VB-groupoids
- Infinitesimal Automorphisms of VB-groupoids and algebroids
- Graded Bundles in the Category of Lie Groupoids
- VB-structures and generalizations
- Glanon groupoids
- Linearization of Poisson groupoids
- Double Principal Bundles
- Lifting statistical structures
- On Hausdorff integrations of Lie algebroids
- Atiyah sequence and Gauge transformations of a principal -bundle over a Lie groupoid
- Multiplicative Connections and Their Lie Theory
- Poisson double structures
- A cohomology theory for Lie 2-algebras
- Shifted coisotropic structures for differentiable stacks
- A cohomological proof for the integrability of strict Lie 2-algebras
- Deformations of symplectic groupoids
- The general linear 2-groupoid
- Lie theory of vector bundles, Poisson geometry and double structures
- Categorification of VB-Lie algebroids and VB-Courant algebroids
- Reduction of symplectic groupoids and quotients of quasi-Poisson manifolds
- Higher Vector Bundles
- Manin triples for double Lie bialgebroids
- Manin triples on multiplicative Courant algebroids