Vector bundles over Lie groupoids and algebroids

@article{Bursztyn2016VectorBO,
  title={Vector bundles over Lie groupoids and algebroids},
  author={H. Bursztyn and A. Cabrera and M. D. Hoyo},
  journal={Advances in Mathematics},
  year={2016},
  volume={290},
  pages={163-207}
}
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. 
Representations up to Homotopy from Weighted Lie Algebroids
Lie theory of vector bundles, Poisson geometry and double structures
Differential forms with values in VB-groupoids
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References

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On the integrability of Lie subalgebroids
Lie groupoids and their orbispaces
On symplectic double groupoids and the duality of Poisson groupoids
General theory of lie groupoids and lie algebroids
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