Modules and representations up to homotopy of Lie n-algebroids
Please always quote using this URN: urn:nbn:de:bvb:20-opus-324333
- 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,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.…
Author: | M. Jotz, R. A. Mehta, T. Papantonis |
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URN: | urn:nbn:de:bvb:20-opus-324333 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Parent Title (English): | Journal of Homotopy and Related Structures |
ISSN: | 2193-8407 |
Year of Completion: | 2023 |
Volume: | 18 |
Issue: | 1 |
Pagenumber: | 23-70 |
Source: | Journal of Homotopy and Related Structures (2023) 18:1, 23-70 DOI: 10.1007/s40062-022-00322-x |
DOI: | https://doi.org/10.1007/s40062-022-00322-x |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | Lie n-algebroids; Poisson algebras; adjoint and coadjoint representations; differential graded modules; representations up to homotopy |
Release Date: | 2024/03/11 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |