Reference : Representations up to Homotopy from Weighted Lie Algebroids
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Representations up to Homotopy from Weighted Lie Algebroids
Bruce, Andrew mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Grabowski, Janusz mailto [nstitute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-656 Warszawa, Poland]
Vitagliano, Luca mailto [Dept. of Mathematics, Università degli Studi di Salerno, Via Giovanni Paolo II n. 123, 84084 Fisciano, Italy]
Journal of Lie Theory
Heldermann Verlag
[en] Graded manifolds ; Lie algebroids ; Lie groupoids
[en] 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.

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