Vector bundles over Lie groupoids and algebroids

2014/10/20 by Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo · 1 citation
Mathematics · #math.DG #math.SG

paper · pdf · doi:10.1016/j.aim.2015.11.044

published as Advances in Mathematics (2016), pp. 163-207 · 37 pages

arxiv created 2014/10/20 · arxiv updated 2016/01/26

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.

Cited by

• Gysin maps and wrong way functoriality via geometric deformation groupoids

Related

• Lie theory of vector bundles, Poisson geometry and double structures
• Deformations of vector bundles in the categories of Lie algebroids and groupoids
• Double Lie algebroids and the double of a Lie bialgebroid
• Deformations of Vector Bundles over Lie Groupoids
• Differential operators and actions of Lie algebroids