@PedroTamaroff I am trying to deform $k[x]$ to a curved dg-algebra with trivial differential but non-trivial curvature and then compute its Hochschild cohomology. In this case I'm afraid that the Koszul resolution doesn't work so we have to stick to the original definition. Hence I am curious how to compute the Hochschild cohomology of $k[x]$ through the original definition.

@A.S. The Deligne conjecture says that the Hochschild cochain has the structure of an $E_2$-algebra, but my question is whether the Hochschild cohomology has the structure of an algebra.