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nuclear fréchet algebra

Proceedings of the Edinburgh Mathematical Society (1)

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Hochschild cohomology of tensor products of topological algebras
Part of
Zinaida A. Lykova
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 2 / June 2010

Published online by Cambridge University Press:

30 April 2010, pp. 447-470
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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.