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Hochschild cohomology of tensor products of topological algebras

Part of: Topological algebras, normed rings and algebras, Banach algebras Lie groups Applied homological algebra and category theory Higher algebraic $K$-theory

Published online by Cambridge University Press:  30 April 2010

Zinaida A. Lykova
Zinaida A. Lykova
Affiliation:
School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, UK ([email protected])
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Abstract

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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.

Keywords

Künneth formulaHochschild homologycyclic homologynuclear DF-spaceslocally convex algebrasnuclear Fréchet algebra

MSC classification

Secondary: 19D55: $K$-theory and homology; cyclic homology and cohomology 22E41: Continuous cohomology 46H40: Automatic continuity 55U25: Homology of a product, Künneth formula
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 2 , June 2010 , pp. 447 - 470
Copyright
Copyright © Edinburgh Mathematical Society 2010