Versal deformation theory of algebras over a quadratic operad

Abstract

We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local algebra as its base--the so called `versal deformation'--which induces all other deformations of the given algebra.

25 pages. To be published in Homology Homotopy and applications