PD Operads and Explicit Partition Lie Algebras

Abstract

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 ${\Sigma }_n$-representations. The derived case requires a further refinement of Koszul duality to a more genuine setting.

To appear in Memoirs of the AMS. 106 pages, 1 figure

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Cited by in corpus (1)

• Pre-Lie algebras with divided powers and the Deligne groupoid in positive characteristic