## Abstract

Let k be a field of characteristic zero, script O sign be a dg operad over k and let A be an script O sign-algebra. In this note we suggest a definition of a formal deformation functor of A Def_{A} : dgart^{≤0}(k) → Δ^{0}Ens from the category of artinian local dg algebras to the category of simplicial sets. This functor generalizes the classical deformation functor for an algebra over a linear operad. In the case script O sign and A are non-positively graded, we prove that Def_{A} is governed by the tangent Lie algebra T_{A} which can be calculated as the Lie algebra of derivations of a cofibrant resolution of A. An example shows that the result does not necessarily hold without the non-positivity condition.

Original language | English |
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Pages (from-to) | 473-494 |

Number of pages | 22 |

Journal | Communications in Algebra |

Volume | 32 |

Issue number | 2 |

DOIs | |

State | Published - 2004 |

## Keywords

- Formal deformations
- Operad algebras
- Simplicial categories
- dg Lie algebra

## ASJC Scopus subject areas

- Algebra and Number Theory