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Representations up to homotopy of Lie algebroids
-
Camilo Arias Abad
and
Marius Crainic
Published/Copyright:
June 17, 2011
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. The relation of this algebra with the integration of Poisson and Dirac structures is explained in [3].
Received: 2009-02-09
Revised: 2010-06-10
Published Online: 2011-06-17
Published in Print: 2012-02
©[2012] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- On counting rings of integers as Galois modules
- On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate
- Invariance of Gromov–Witten theory under a simple flop
- Representations up to homotopy of Lie algebroids
- Counting lattice points
- Cyclic homology of strong smash product algebras
- Ancient solutions of Ricci flow on spheres and generalized Hopf fibrations
Articles in the same Issue
- On counting rings of integers as Galois modules
- On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate
- Invariance of Gromov–Witten theory under a simple flop
- Representations up to homotopy of Lie algebroids
- Counting lattice points
- Cyclic homology of strong smash product algebras
- Ancient solutions of Ricci flow on spheres and generalized Hopf fibrations
