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Hochschild homology criteria for trivial algebra structures |
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| Authors: | Micheline Vigué -Poirrier |
| Affiliation: | Université Paris-Nord, Institut Galilée, Département de Mathématiques, F-93430 Villetaneuse, France |
| 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  be a 1-connected finite CW-complex. We characterize the trivial algebra structure on the cohomology algebra of  with coefficients in a fixed field in terms of the maximality of the Betti numbers of the free loop space. |
| Keywords: | Augmented algebra Hochschild homology cyclic homology free loop space minimal model of a differential graded algebra |
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