Deformations of homotopy algebras

Details Deformations of homotopy algebras Deformations of homotopy algebras

1999-04-26

arxiv.org/abs/math/9904145v1

Mathematics

Algebraic Geometry

14 pages, latex

Scientific paper

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 $$\Def_A:\dgar(k)\to\simpl$$ 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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