Homology, Homotopy and Applications

On the classification of Moore algebras and their deformations

Alastair Hamilton

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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.

Article information

Homology Homotopy Appl., Volume 6, Number 1 (2004), 87-107.

First available in Project Euclid: 13 February 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16E45: Differential graded algebras and applications
Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 18G99: None of the above, but in this section


Hamilton, Alastair. On the classification of Moore algebras and their deformations. Homology Homotopy Appl. 6 (2004), no. 1, 87--107. https://projecteuclid.org/euclid.hha/1139839546

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