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Article Dans Une Revue Journal of the London Mathematical Society Année : 2022

Moduli problems for operadic algebras

Résumé

A theorem of Pridham and Lurie provides an equivalence between formal moduli problems and Lie algebras in characteristic zero. We prove a generalization of this correspondence, relating formal moduli problems parametrized by algebras over a Koszul operad to algebras over its Koszul dual operad. In particular, when the Lie algebra associated to a deformation problem is induced from a pre-Lie structure it corresponds to a permutative formal moduli problem. As another example we obtain a correspondence between operadic formal moduli problems and augmented operads.

Dates et versions

hal-02440283 , version 1 (15-01-2020)

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Citer

Damien Calaque, Ricardo Campos, Joost Nuiten. Moduli problems for operadic algebras. Journal of the London Mathematical Society, 2022, 106 (4), pp.3450-3544. ⟨10.1112/jlms.12666⟩. ⟨hal-02440283⟩
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