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- W4287907392 abstract "This paper studies differential graded modules and representations up to homotopy of Lie $n$-algebroids, for general $ninmathbb{N}$. 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." @default.
- W4287907392 created "2022-07-26" @default.
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- W4287907392 date "2020-01-04" @default.
- W4287907392 modified "2023-09-26" @default.
- W4287907392 title "Modules and representations up to homotopy of Lie $n$-algebroids" @default.
- W4287907392 doi "https://doi.org/10.48550/arxiv.2001.01101" @default.
- W4287907392 hasPublicationYear "2020" @default.
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