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


Alice Fialowski (Institute of Mathematics, Eotvos Lorand University, Budapest, Hungary)

Goutam Mukherjee (Stat-Math Unit, Indian Statistical Institute, Calcutta, India)

Anita Naolekar (Stat-Math Unit, Indian Statistical Institute, Bangalore, India)


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.


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

2010 Mathematics Subject Classification

17Axx, 18D50, 18G50

Published 2 June 2014