10 jul 2017 -- 15:00
Università degli Studi di Salerno - Sala riunioni DipMat
Abstract.
Lie groupoids, and their infinitesimal counterparts Lie algebroids, naturally appear in many areas of geometry. In particular the Lie theory of Lie groupoids and Lie algebroids goes far beyond the classical results for Lie groups and algebras.
In this talk we will give a brief introduction to VB-groupoids, and their infinitesimal counterpart VB-algebroids. In recent years these objects have been intensively studied in view of their relevant role both in Poisson geometry and the theory of representions of Lie groupoids and algebroids. VB-groupoids (VB-algebroids) can be seen both as vector bundle objects in the category of Lie groupoids (algebroids) and as Lie groupoid (algebroid) objects in the category of vector bundles.
The final objective of this talk will be to describe the Lie theory of VB-groupoids and VB-algebroids. In doing this we will take full advantage of the equivalent characterization of VB-groupoids (algebroids) as Lie groupoids (algebroids) additionally equipped with compatible homogeneity structures.