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# Homology, Homotopy and Applications

## Volume 16 (2014)

### Number 1

### Versal deformation theory of algebras over a quadratic operad

Pages: 179 – 198

DOI: https://dx.doi.org/10.4310/HHA.2014.v16.n1.a11

#### Authors

#### 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.

#### Keywords

operad, algebra, cohomology, versal, deformation, obstruction, convolution Lie algebra, Maurer-Cartan element

#### 2010 Mathematics Subject Classification

17Axx, 18D50, 18G50

Published 2 June 2014