Geodesic
Representations up to Homotopy from Weighted Lie Algebroids
Journal of Lie theory, Tome 28 (2018) no. 3, pp. 711-733
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Weighted Lie algebroids were recently introduced as Lie algebroids equipped with an additional compatible non-negative grading, and represent a wide generalisation of the notion of a VB-algebroid. There is a close relation between two term representations up to homotopy of Lie algebroids and VB-algebroids. In this paper we show how this relation generalises to weighted Lie algebroids and in doing so we uncover new and natural examples of higher term representations up to homotopy of Lie algebroids. Moreover, we show how the van Est theorem generalises to weighted objects.
Classification : 16W50, 22A22, 53D17
Mots-clés : Graded manifolds, Lie algebroids, Lie groupoids, representations up to homotopy 
@article{JLT_2018_28_3_JLT_2018_28_3_a6,
     author = {A. J. Bruce and J. Grabowski and L. Vitagliano},
     title = {Representations up to {Homotopy} from {Weighted} {Lie} {Algebroids}},
     journal = {Journal of Lie theory},
     pages = {711--733},
     year = {2018},
     volume = {28},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_3_JLT_2018_28_3_a6/}
}
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A. J. Bruce; J. Grabowski; L. Vitagliano. Representations up to Homotopy from Weighted Lie Algebroids. Journal of Lie theory, Tome 28 (2018) no. 3, pp. 711-733. http://geodesic.mathdoc.fr/item/JLT_2018_28_3_JLT_2018_28_3_a6/