Journal of Lie Theory

no. 3
Representations up to Homotopy from Weighted Lie Algebroids
Andrew James Bruce1; Janusz Grabowski2; Luca Vitagliano3
1Mathematics Research Unit, University of Luxembourg, Maison du Nombre, 6 Avenue de la Fonte, 4364 Esch-sur-Alzette, Luxembourg
2Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-656 Warszawa, Poland
3Dept. of Mathematics, Università degli Studi di Salerno, Via Giovanni Paolo II n. 123, 84084 Fisciano, Italy
Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 711-733
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.
DOI: 10.5802/jolt.1022
Classification: 16W50, 22A22, 53D17
Keywords: Graded manifolds, Lie algebroids, Lie groupoids, representations up to homotopy

Andrew James Bruce  1 ; Janusz Grabowski  2 ; Luca Vitagliano  3

1 Mathematics Research Unit, University of Luxembourg, Maison du Nombre, 6 Avenue de la Fonte, 4364 Esch-sur-Alzette, Luxembourg
2 Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-656 Warszawa, Poland
3 Dept. of Mathematics, Università degli Studi di Salerno, Via Giovanni Paolo II n. 123, 84084 Fisciano, Italy 
Andrew James Bruce; Janusz Grabowski; Luca Vitagliano. Representations up to Homotopy from Weighted Lie Algebroids. Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 711-733. doi: 10.5802/jolt.1022
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     title = {Representations up to {Homotopy} from {Weighted} {Lie} {Algebroids}},
     journal = {Journal of Lie Theory},
     pages = {711--733},
     year = {2018},
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