PD Operads and Explicit Partition Lie Algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909380905009152 |
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| author | Brantner, Lukas Campos, Ricardo Nuiten, Joost |
| author_facet | Brantner, Lukas Campos, Ricardo Nuiten, Joost |
| contents | Infinitesimal deformations are governed by partition Lie algebras. In characteristic $0$, these higher categorical structures are modelled by differential graded Lie algebras, but in characteristic $p$, they are more subtle. We give explicit models for partition Lie algebras over general coherent rings, both in the setting of spectral and derived algebraic geometry. For the spectral case, we refine operadic Koszul duality to a functor from operads to divided power operads, by taking refined linear duals of $Σ_n$-representations. The derived case requires a further refinement of Koszul duality to a more genuine setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_03870 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | PD Operads and Explicit Partition Lie Algebras Brantner, Lukas Campos, Ricardo Nuiten, Joost Algebraic Geometry Algebraic Topology 14D23, 14D15, 18M70, 18N70, 17B55, 13A35 Infinitesimal deformations are governed by partition Lie algebras. In characteristic $0$, these higher categorical structures are modelled by differential graded Lie algebras, but in characteristic $p$, they are more subtle. We give explicit models for partition Lie algebras over general coherent rings, both in the setting of spectral and derived algebraic geometry. For the spectral case, we refine operadic Koszul duality to a functor from operads to divided power operads, by taking refined linear duals of $Σ_n$-representations. The derived case requires a further refinement of Koszul duality to a more genuine setting. |
| title | PD Operads and Explicit Partition Lie Algebras |
| topic | Algebraic Geometry Algebraic Topology 14D23, 14D15, 18M70, 18N70, 17B55, 13A35 |
| url | https://arxiv.org/abs/2104.03870 |