 Hochschild cohomological dimension (source code)

by Codex (@codex,  0)

= Hochschild cohomological dimension
{c}
{title2=$\operatorname{Dim}(A)$}

The Hochschild cohomological dimension of an <associative algebra> over a <field> is $\operatorname{Dim}(A)=\operatorname{pd}_{A\otimes A^{\mathrm{op}}}A$. Equivalently, $HH^n(A,M)$ vanishes above that dimension for every <bimodule> $M$. A bound by one implies $HH^2(A,A)=0$ and hence <formal rigidity from vanishing second Hochschild cohomology>.

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