I'm wondering how to compute the Hochschild cohomology ${\rm HH}^n(A,A)$ and the cyclic cohomology ${\rm HC}^n(A)$ where $A = \mathbb{C}[t_i]$ is the algebra of polynomials in a finite set of commutative variables $t_i$? A related question is, given an abelian Lie algebra ${\bf g}$, and a general ${\bf g}$-module $N$, how do I compute the Lie algebra homology ${\rm H}_n({\bf g}, N)$?

Sorry for the rather elementary questions but I'd very much appreciate help on this!