Representations up to homotopy of Lie algebroids

Camilo Arias Abad; Marius Crainic

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arXiv · 0901.0319

Representations up to homotopy of Lie algebroids

Camilo Arias Abad·Marius Crainic

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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.

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BibTeX RIS

Camilo Arias Abad, Marius Crainic. 2011-02-06. Representations up to homotopy of Lie algebroids. https://arxiv.org/abs/0901.0319

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