Vector bundles over Lie groupoids and algebroids
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo

TL;DR
This paper explores the theory of vector bundles over Lie groupoids and algebroids, clarifying their relationships through differentiation and integration, and extending techniques to more complex structures like double Lie algebroids.
Contribution
It provides a new reformulation of VB-groupoids and VB-algebroids, elucidates their Lie theory relations, and extends methods to double Lie algebroids and LA-groupoids.
Findings
Reformulated definitions of VB-groupoids and VB-algebroids
Clarified their relation via Lie theory
Extended techniques to double Lie algebroids and LA-groupoids
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
