Publication: Representations up to homotopy of Lie algebroids
Representations up to homotopy of Lie algebroids
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Abad, C. A., & Crainic, M. (2012). Representations up to homotopy of Lie algebroids. Journal Für Die Reine Und Angewandte Mathematik, 2012, 91–126. https://doi.org/10.1515/crelle.2011.095
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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 e
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- Abad, C A
- Crainic, M
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Abad, C. A., & Crainic, M. (2012). Representations up to homotopy of Lie algebroids. Journal Für Die Reine Und Angewandte Mathematik, 2012, 91–126. https://doi.org/10.1515/crelle.2011.095
