[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.
Disciplines :
Mathematics
Author, co-author :
Bruce, Andrew ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Grabowski, Janusz; nstitute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-656 Warszawa, Poland
Vitagliano, Luca; Dept. of Mathematics, Università degli Studi di Salerno, Via Giovanni Paolo II n. 123, 84084 Fisciano, Italy
External co-authors :
yes
Language :
English
Title :
Representations up to Homotopy from Weighted Lie Algebroids