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arXiv · 1609.09384

A Lower-Bound on the Hochschild Cohomological Dimension

Anastasis Kratsios
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Abstract

A concrete lower-bound for the Hochschild cohomological dimension of a commutative $k$-algebra, in terms of three other homological invariants is obtained. This result is then used to show that most $k$-algebras fail to be quasi-free, even if they are smooth. This result generalizes a result of \cite{cuntz1995algebra} to the case where the base-ring is no longer $\cc$ but can be any commutative ring with unity.

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Anastasis Kratsios. 2016-09-29. A Lower-Bound on the Hochschild Cohomological Dimension. https://doi.org/10.3390/math9030251

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