Homology, Homotopy and Applications

Versal deformation theory of algebras over a quadratic operad

Alice Fialowski, Goutam Mukherjee, and Anita Naolekar

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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.

Article information

Source
Homology Homotopy Appl., Volume 16, Number 1 (2014), 179-198.

Dates
First available in Project Euclid: 3 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.hha/1401800079

Mathematical Reviews number (MathSciNet)
MR3211742

Zentralblatt MATH identifier
1306.18003

Subjects
Primary: 18D50: Operads [See also 55P48] 17Axx: General nonassociative rings 18G50: Nonabelian homological algebra

Keywords
Operad algebra cohomology versal deformation obstruction convolution Lie algebra Maurer-Cartan element

Citation

Fialowski, Alice; Mukherjee, Goutam; Naolekar, Anita. Versal deformation theory of algebras over a quadratic operad. Homology Homotopy Appl. 16 (2014), no. 1, 179--198. https://projecteuclid.org/euclid.hha/1401800079


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