Hochschild cohomology of tensor products of topological algebras

Abstract

We describe explicitly the continuous Hochschild and cyclic cohomology groups of certain tensor products of ⊗-algebras which are Fréchet spaces or nuclear DF -spaces. To this end we establish the existence of topological isomorphisms in the Künneth formula for the cohomology of complete nuclear DF -complexes and in the Künneth formula for continuous Hochschild cohomology of nuclear ⊗-algebras which are Fréchet spaces or DF -spaces for which all boundary maps of the standard homology complexes have closed ranges.