Paper "Modules and representations up to homotopy of Lie n-algebroids" published in Journal of Homotopy and Related Structures.

The paper "Modules and representations up to homotopy of Lie n-algebroids" by M. Jotz, R. Mehta and T. Papatonis has appeared in the 'Journal of homotopy and related structures'. 

See here.

This paper studies differential graded modules and representations up to homotopy of Lie n-algebroids, for general . 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.