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Cyclic cohomology of certain nuclear Fréchet and DF algebras

Lookup NU author(s): Dr Zinaida LykovaORCiD


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We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain ×̂-algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuous morphism ψ: x → y of complexes of complete nuclear DF-spaces, the isomorphism of cohomology groups Hn(ψ): Hn (x) → Hn(y) is automatically topological. The continuous cyclic-type homology and cohomology are described up to topological isomorphism for the following classes of biprojective ×-algebras: the tensor algebra E×F generated by the duality (E,F, 〈·,·〉) for nuclear Fréchet spaces E and F or for nuclear DF-spaces E and F; nuclear biprojective Köthe algebras λ(P) which are Fréchet spaces or DF-spaces; the algebra of distributions ε* (G) on a compact Lie group G. © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2008.

Publication metadata

Author(s): Lykova ZA

Publication type: Article

Publication status: Published

Journal: Central European Journal of Mathematics

Year: 2008

Volume: 6

Issue: 3

Pages: 405-421

Date deposited: 28/04/2011

ISSN (print): 1895-1074

ISSN (electronic): 1644-3616

Publisher: Versita


DOI: 10.2478/s11533-008-0040-x


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