Hochschild cohomology of tensor products of topological algebras

Abstract

AbstractWe describe explicitly the continuous Hochschild and cyclic cohomology groups of certain tensor products of $\widehat{\otimes}$-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 $\widehat{\otimes}$-algebras which are Fréchet spaces or DF-spaces for which all boundary maps of the standard homology complexes have closed ranges.