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Article Dans Une Revue Memoirs of the American Mathematical Society Année : 2025

PD Operads and Explicit Partition Lie Algebras

Résumé

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 Σn-representations. The derived case requires a further refinement of Koszul duality to a more genuine setting.

Dates et versions

hal-03229237 , version 1 (18-05-2021)

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Lukas Brantner, Ricardo Campos, Joost Nuiten. PD Operads and Explicit Partition Lie Algebras. Memoirs of the American Mathematical Society, In press. ⟨hal-03229237⟩
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