Representations up to homotopy of Lie algebroids

Abstract

We introduce and study the notion of representation up to homotopy of a Lie algebroid, paying special attention to examples. We use representations up to homotopy to define the adjoint representation of a Lie algebroid and show that the resulting cohomology controls the deformations of the structure. The Weil algebra of a Lie algebroid is defined and shown to coincide with Kalkman's BRST model for equivariant cohomology in the case of group actions.

29 pages. Final version, to appear in "Journal für die reine und angewandte Mathematik"

References in corpus (1)

• On the perturbation lemma, and deformations

Cited by in corpus (14)

• Twisted differential String and Fivebrane structures
• Lie algebroid structures on double vector bundles and representation theory of Lie algebroids
• Generalized Kahler geometry
• Representations of Homotopy Lie-Rinehart Algebras
• Integration of Exact Courant Algebroids
• L-infinity algebra actions
• Knot Invariants and New Weight Systems from General 3D TFTs
• On the role of effective representations of Lie groupoids
• The A_infty de Rham theorem and integration of representations up to homotopy
• The Weil algebra and the Van Est isomorphism
• Deformations of Lie brackets and representations up to homotopy
• Semidirect products of representations up to homotopy
• On deformations of Lie algebroids
• 2D and 3D topological field theories for generalized complex geometry