Higher Extensions of Lie Algebroids

Abstract

We study the extension of a Lie algebroid by a representation up to homotopy, including semidirect products of a Lie algebroid with such representations. The extension results in a higher Lie algebroid. We give exact Courant algebroids and string Lie 2-algebras as examples of such extensions. We then apply this to obtain a Lie 2-groupoid integration of an exact Courant algebroid.

32 pages

References in corpus (4)

• On the category of Lie n-algebroids
• From double Lie groupoids to local Lie 2-groupoids
• Lie algebroid modules and representations up to homotopy
• VB-algebroid morphisms and representations up to homotopy

Cited by in corpus (13)

• Extended Riemannian Geometry I: Local Double Field Theory
• Shifted derived Poisson manifolds associated with Lie pairs
• Homotopical algebra for Lie algebroids
• Global Aspects of Doubled Geometry and Pre-rackoid
• Deformation spaces and normal forms around transversals
• Lie 2-algebroids and matched pairs of 2-representations - a geometric approach
• The geometry of graded cotangent bundles
• Cohomologies and crossed modules for pre-Lie Rinehart algebras
• Graded Lie-Rinehart algebras
• The van Est homomorphism for strict Lie 2-groups
• The first Pontryagin class of a quadratic Lie 2-algebroid
• Quantization of (-1)-Shifted Derived Poisson Manifolds
• Categorification of VB-Lie algebroids and VB-Courant algebroids