Moduli problems for operadic algebras
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 preLie structure it corresponds to a permutative formal moduli problem. As another example we obtain a correspondence between operadic formal moduli problems and augmented operads.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.13495
 Bibcode:
 2019arXiv191213495C
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Algebraic Geometry;
 Mathematics  Category Theory;
 Mathematics  Quantum Algebra;
 55P10;
 18D50;
 55P48;
 14D15
 EPrint:
 Slight expansion of operadic deformation theory and some minor changes