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Representations up to homotopy of Lie algebroids

Abad, Camilo Arias ; Crainic, Marius

In: Journal für die reine und angewandte Mathematik (Crelles Journal), 2012, vol. 2012, no. 663, p. 91-126

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    Titre
    • Representations up to homotopy of Lie algebroids
    Auteur
    • Abad, Camilo Arias. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
    • Crainic, Marius. Mathematics Institute, Utrecht University, 3508 TA Utrecht, The Netherlands
    Type de document
    • Postprint
    Langue
    • Inglese
    Publié dans
    • Journal für die reine und angewandte Mathematik (Crelles Journal), 2012, vol. 2012, no. 663, p. 91-126. De Gruyter
    Autre version électronique
    Classification
    • Santé
    Identifiant OAI-PMH
    • oai:doc.rero.ch:295849
    Summary
    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]