Document Type
Article
Publication Date
1-5-2023
Publication Title
Journal of Homotopy and Related Structures
Abstract
This paper studies differential graded modules and representations up to homotopy of Lie n-algebroids, for general n ∈ 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, theWeil 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.
Keywords
Lie n-algebroids, Representations up to homotopy, Differential graded modules, Poisson algebras, Adjoint and coadjoint representations
Volume
18
First Page
23
Last Page
70
DOI
10.1007/s40062-022-00322-x
Rights
© The Author(s) 2022
Recommended Citation
Jotz, M.; Mehta, Rajan Amit; and Papantonis, T., "Modules and Representations up to Homotopy of Lie n-Algebroids" (2023). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/176
Comments
Archived as published. Open access article.