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.
- Pub Date:
- December 2019
- Mathematics - Algebraic Topology;
- Mathematics - Algebraic Geometry;
- Mathematics - Category Theory;
- Mathematics - Quantum Algebra;
- Slight expansion of operadic deformation theory and some minor changes