I really want to know more about Hochschild cohomology of commutative algebras, and its relation to the representations of $S_n$ and to free Lie algebras (beyound "there are these strange idempotents in $\mathbb Q\left[S_n\right]$ which happen to occur in both fields).

I really want to know more about Hochschild cohomology of commutative algebras, and its relation to the representations of $S_n$ and to free Lie algebras (beyond "there are these strange idempotents in $\mathbb Q\left[S_n\right]$ which happen to occur in both fields).