Deformations of homotopy algebras
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 $$\Def_A:\dgar(k)\to\simpl$$ from the category of artinian local dg algebras to the category of simplicial sets. In the case $\CO$ and $A$ are nonpositively 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 1999
 arXiv:
 arXiv:math/9904145
 Bibcode:
 1999math......4145H
 Keywords:

 Algebraic Geometry;
 Quantum Algebra
 EPrint:
 14 pages, latex