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Representations up to homotopy of Lie algebroids


Abad, C A; Crainic, M (2012). Representations up to homotopy of Lie algebroids. Journal für die Reine und Angewandte Mathematik, 2012(663):91-126.

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 [Arias Abad, Crainic, Ann. Inst. Fourier].

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 [Arias Abad, Crainic, Ann. Inst. Fourier].

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:January 2012
Deposited On:17 Feb 2012 18:26
Last Modified:16 Feb 2018 23:19
Publisher:Walter de Gruyter
ISSN:0075-4102 (P) 1435-5345 (E)
OA Status:Green
Publisher DOI:https://doi.org/10.1515/crelle.2011.095
Related URLs:http://arxiv.org/abs/0901.0319

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