Infinitesimal Automorphisms of VB-groupoids and algebroids
arXiv:1611.06896 · doi:10.1093/qmath/haz007
Abstract
VB-groupoids and algebroids are vector bundle objects in the categories of Lie groupoids and Lie algebroids respectively, and they are related via the Lie functor. VB-groupoids and algebroids play a prominent role in Poisson and related geometries. Additionally, they can be seen as models for vector bundles over singular spaces. In this paper we study their infinitesimal automorphisms, i.e. vector fields on them generating a flow by diffeomorphisms preserving both the linear and the groupoid/algebroid structures. For a special class of VB-groupoids/algebroids coming from representations of Lie groupoids/algebroids, we prove that infinitesimal automorphisms are the same as multiplicative sections of a certain derivation groupoid/algebroid.
arXiv commentv4: 44 pages, several revisions, final version to appear in Q. J. Math., comments very welcome
References in corpus (25)
- Higher vector bundles and multi-graded symplectic manifolds
- Generalized Lie bialgebroids and Jacobi structures
- Lie algebroid structures on double vector bundles and representation theory of Lie algebroids
- Vector bundles over Lie groupoids and algebroids
- VB-groupoids and representation theory of Lie groupoids
- Poisson Quasi-Nijenhuis Manifolds
- -Manifolds and Mackenzie Theory
- Representations of Homotopy Lie-Rinehart Algebras
- Lie theory of multiplicative tensors
- Remarks on Contact and Jacobi Geometry
- Multiplicative Dirac structures on Lie groups
- Lie algebroid modules and representations up to homotopy
- Generalized Contact Bundles
- Q-groupoids and their cohomology
- Deformations of Lie groupoids
- VB-algebroid morphisms and representations up to homotopy
- Van Est isomorphism for homogeneous cochains
- Lie brackets on affine bundles
- Differential forms with values in VB-groupoids
- Multiplicative Dirac structures
- Jacobi bundles and the BFV-complex
- Deformations of Linear Lie Brackets
- Glanon groupoids
- On the integration of LA-groupoids and duality for Poisson groupoids
- Integration of generalized complex structures