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# Homology, Homotopy and Applications

## Volume 6 (2004)

### Number 1

### On the classification of Moore algebras and their deformations

Pages: 87 – 107

DOI: http://dx.doi.org/10.4310/HHA.2004.v6.n1.a7

#### Author

#### Abstract

In this paper we will study deformations of $A_{\infty}$-algebras. We will also answer questions relating to Moore algebras which are one of the simplest nontrivial examples of an $A_{\infty}$-algebra. We will compute the truncated Hochschild cohomology of odd Moore algebras and classify them up to a unital weak equivalence. We will construct miniversal deformations of particular Moore algebras and relate them to the universal odd and even Moore algebras. Finally we will conclude with an investigation of formal one-parameter deformations of an $A_{\infty}$-algebra.

#### Keywords

$A_{\infty}$-algebra, Moore algebra, Hochschild cohomology, deformation, power series

#### 2010 Mathematics Subject Classification

13D10, 13F25, 13N15, 14J10, 16E45