Moduli problems for operadic algebras
Algebraic Topology
2023-07-04 v3 Algebraic Geometry
Category Theory
Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.1912.13495,
title = {Moduli problems for operadic algebras},
author = {Damien Calaque and Ricardo Campos and Joost Nuiten},
journal= {arXiv preprint arXiv:1912.13495},
year = {2023}
}
Comments
Major reorganization of the paper in order to increase readability. No change to main results, but some examples were added. To appear on JLMS