ON SOME 2ND-HOCHSCHILD COHOMOLOGY SPACES FOR ALGEBRAS OF FUNCTIONS ONA MANIFOLD

We show that the second Hochschild cohomology space for the space of s mooth functions on a manifold corresponding to cochains defined by con tinuous operators is the same as the one corresponding to differentiab le operators, i.e. is given by the space of skewsymmetric contravarian t 2-tensors on the manifold. We do this using a coboundary constructio n due to Omori, Maeda and Yoshioka.