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Transactions of the American Mathematical Society

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Hochschild homology criteria for trivial algebra structures


Author: Micheline Vigué-Poirrier
Journal: Trans. Amer. Math. Soc. 354 (2002), 3869-3882
MSC (2000): Primary 13N05, 18F25, 55P62
DOI: https://doi.org/10.1090/S0002-9947-02-03053-2
Published electronically: June 4, 2002
MathSciNet review: 1926856
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Abstract: We prove two similar results by quite different methods. The first one deals with augmented artinian algebras over a field: we characterize the trivial algebra structure on the augmentation ideal in terms of the maximality of the dimensions of the Hochschild homology (or cyclic homology) groups. For the second result, let $X$ be a 1-connected finite CW-complex. We characterize the trivial algebra structure on the cohomology algebra of $X$ with coefficients in a fixed field in terms of the maximality of the Betti numbers of the free loop space.


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Additional Information

Micheline Vigué-Poirrier
Affiliation: Université Paris-Nord, Institut Galilée, Département de Mathématiques, F-93430 Villetaneuse, France
Email: vigue@math.univ-paris13.fr

DOI: https://doi.org/10.1090/S0002-9947-02-03053-2
Keywords: Augmented algebra, Hochschild homology, cyclic homology, free loop space, minimal model of a differential graded algebra
Received by editor(s): March 23, 2001
Received by editor(s) in revised form: March 15, 2002
Published electronically: June 4, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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