Deformations of homotopy algebras

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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 DefA : dgart≤0(k) → Δ0Ens 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 DefA is governed by the tangent Lie algebra TA 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 languageEnglish
Pages (from-to)473-494
Number of pages22
JournalCommunications in Algebra
Issue number2
StatePublished - 2004


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

ASJC Scopus subject areas

  • Algebra and Number Theory


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