TY  - JOUR
A1  - Jotz, M.
A1  - Mehta, R. A.
A1  - Papantonis, T.
T1  - Modules and representations up to homotopy of Lie n-algebroids
JF  - Journal of Homotopy and Related Structures
N2  - This paper studies differential graded modules and representations up to homotopy of Lie n-algebroids, for general \(n\in {\mathbb {N}}\). The adjoint and coadjoint modules are described, and the corresponding split versions of the adjoint and coadjoint representations up to homotopy are explained. In particular, the case of Lie 2-algebroids is analysed in detail. The compatibility of a Poisson bracket with the homological vector field of a Lie n-algebroid is shown to be equivalent to a morphism from the coadjoint module to the adjoint module, leading to an alternative characterisation of non-degeneracy of higher Poisson structures. Moreover, the Weil algebra of a Lie n-algebroid is computed explicitly in terms of splittings, and representations up to homotopy of Lie n-algebroids are used to encode decomposed VB-Lie n-algebroid structures on double vector bundles.
KW  - Lie n-algebroids
KW  - representations up to homotopy
KW  - differential graded modules
KW  - Poisson algebras
KW  - adjoint and coadjoint representations
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-324333
SN  - 2193-8407
VL  - 18
IS  - 1
ER  -