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Relative cohomology of Banach algebras

Lookup NU author(s): Dr Zinaida LykovaORCiD


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Let A be a Banach algebra, not necessarily unital, and let B be a closed subalgebra of A. We establish a connection between the Banach cyclic cohomology group HCn(A) of A and the Banach B-relative cyclic cohomology group HCBn(A) of A. We prove that, for a Banach algebra A with a bounded approximate identity and an amenable closed subalgebra B of A, up to topological isomorphism, HCn(A) = HCBn(A) for all n greater than or equal to 0. We also establish a connection between the Banach simplicial or cyclic cohomology groups of A and those of the quotient algebra A/I by an amenable closed bi-ideal I. The results are applied to the calculation of these groups for certain operator algebras, including von Neumann algebras and joins of operator algebras.

Publication metadata

Author(s): Lykova ZA

Publication type: Article

Publication status: Published

Journal: Journal of Operator Theory

Year: 1999

Volume: 41

Issue: 1

Pages: 23-53

Print publication date: 01/01/1999

ISSN (print): 0379-4024

ISSN (electronic):

Publisher: Academia Romana