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Let $HH_*(A,N)$ (or $HH^*(A,N)$) be the Hochschild homology (or cohomology) of an associative algebra $A$ with coefficients in an $A$-bimodule $N$. I was reading nlab's entry on Hochschild cohomology ...

I recently heard a talk about these topics and found them very interesting. The talk was centered on the formal structure and didn't really focus on examples. So my question is: what is your favorite ...