Modules and representations up to homotopy of Lie n-algebroids
Zitieren Sie bitte immer diese 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.…
Autor(en): | M. Jotz, R. A. Mehta, T. Papantonis |
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URN: | urn:nbn:de:bvb:20-opus-324333 |
Dokumentart: | Artikel / Aufsatz in einer Zeitschrift |
Institute der Universität: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Sprache der Veröffentlichung: | Englisch |
Titel des übergeordneten Werkes / der Zeitschrift (Englisch): | Journal of Homotopy and Related Structures |
ISSN: | 2193-8407 |
Erscheinungsjahr: | 2023 |
Band / Jahrgang: | 18 |
Heft / Ausgabe: | 1 |
Seitenangabe: | 23-70 |
Originalveröffentlichung / Quelle: | 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 |
Allgemeine fachliche Zuordnung (DDC-Klassifikation): | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Freie Schlagwort(e): | Lie n-algebroids; Poisson algebras; adjoint and coadjoint representations; differential graded modules; representations up to homotopy |
Datum der Freischaltung: | 11.03.2024 |
Lizenz (Deutsch): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |