@article{JotzMehtaPapantonis2023,
  author    = {Jotz, M. and Mehta, R. A. and Papantonis, T.},
  title     = {Modules and representations up to homotopy of Lie n-algebroids},
  series = {Journal of Homotopy and Related Structures},
  volume    = {18},
  journal   = {Journal of Homotopy and Related Structures},
  number    = {1},
  issn      = {2193-8407},
  doi       = {10.1007/s40062-022-00322-x},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-324333},
  pages     = {23-70},
  year      = {2023},
  abstract  = {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.},
  language  = {en}
}