ON THE HOCHSCHILD COHOMOLOGY OF CROSSED-PRODUCTS

In this paper we show that there exists a spectral sequence with E2p,q congruent-to H(p)(G, H(q)(LAMBDA, A)) approximating H(p+q)(GAMMA, A) the Hochschild cohomology of crossed products GAMMA = (LAMBDA, G, theta) and that an isomorphism E(infinity)p,q congruent-to F(p)H(p+q)(GAMMA, A)/F(p+1)H(p+q)(GAMMA, A) preserves products. As an example, we determine the module structure of the Hochschild cohomology of a certain crossed product and also the ring structure in a special case.