Hochschild homology criteria for trivial algebra structures

Vigué-Poirrier, Micheline

doi:10.1090/S0002-9947-02-03053-2

Hochschild homology criteria for trivial algebra structures
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by Micheline Vigué-Poirrier PDF

Trans. Amer. Math. Soc. 354 (2002), 3869-3882 Request permission

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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