Actions of Lie 2-algebras and comomentum maps
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908836352229376 |
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| author | Bonneau, Philippe Chloup-Arnould, Véronique Gammella, Angela Wurzbacher, Tilmann |
| author_facet | Bonneau, Philippe Chloup-Arnould, Véronique Gammella, Angela Wurzbacher, Tilmann |
| contents | In this paper we introduce the notion of a 2-action of a Lie 2-algebra on an arbitrary manifold M. Furthermore, in [Rog12], given a n-plectic manifold (M, $ω$), the authors consider a Lie Infinity-algebra L$\infty$ (M, $ω$), which is a higher analogue of the Poisson algebra of observables associated to a symplectic manifold. This Lie Infinity-algebra reduces to a Lie 2-algebra L^2 (M, $ω$) when (M, $ω$) is 2-plectic. Following ideas of N.L. Delgado [Del18], we introduce the Lie 2-algebra D^2 (M, $ω$), which generalises the Lie 2-algebra L^2 (M, $ω$) and its extension containing Hamiltonian pairs. Given a two-plectic manifold (M, $ω$) and a Lie 2-algebra g_1 $\oplus$ g_0 acting on M we define a comomentum map as a lift of the action, i.e., as a Lie 2-algebra morphism from g_1 $\oplus$ g_0 to the extension of the Lie 2-algebra D^2 (M, $ω$). In an appendix, we discuss very explicitly numerous examples, classified according to their algebraic properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14715 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Actions of Lie 2-algebras and comomentum maps Bonneau, Philippe Chloup-Arnould, Véronique Gammella, Angela Wurzbacher, Tilmann Mathematical Physics Rings and Algebras Symplectic Geometry In this paper we introduce the notion of a 2-action of a Lie 2-algebra on an arbitrary manifold M. Furthermore, in [Rog12], given a n-plectic manifold (M, $ω$), the authors consider a Lie Infinity-algebra L$\infty$ (M, $ω$), which is a higher analogue of the Poisson algebra of observables associated to a symplectic manifold. This Lie Infinity-algebra reduces to a Lie 2-algebra L^2 (M, $ω$) when (M, $ω$) is 2-plectic. Following ideas of N.L. Delgado [Del18], we introduce the Lie 2-algebra D^2 (M, $ω$), which generalises the Lie 2-algebra L^2 (M, $ω$) and its extension containing Hamiltonian pairs. Given a two-plectic manifold (M, $ω$) and a Lie 2-algebra g_1 $\oplus$ g_0 acting on M we define a comomentum map as a lift of the action, i.e., as a Lie 2-algebra morphism from g_1 $\oplus$ g_0 to the extension of the Lie 2-algebra D^2 (M, $ω$). In an appendix, we discuss very explicitly numerous examples, classified according to their algebraic properties. |
| title | Actions of Lie 2-algebras and comomentum maps |
| topic | Mathematical Physics Rings and Algebras Symplectic Geometry |
| url | https://arxiv.org/abs/2602.14715 |