Deformations of homotopy algebras

1999/04/26 by V. Hinich, Hinich, V.
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #math.AG #math.QA

paper · pdf · doi:10.48550/arxiv.math/9904145

14 pages, latex

arxiv created 1999/04/26 · arxiv updated 2009/11/30

Abstract

Let k be a field of characteristic zero, \CO be a dg operad over k and let A be an \CO-algebra. In this note we define formal deformations of A, construct the deformation functor \Def_A:\dgar(k)→\simpl from the category of artinian local dg algebras to the category of simplicial sets. In the case \CO and A are non-positively graded, we prove that \Def_A is governed by the tangent Lie algebra T_A (defined as derivations of a cofibrant resolution of A). A very easy example shows that the result does not hold without this condition.

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