ON EXCISION IN PERIODIC CYCLIC COHOMOLOGY
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Output type: Journal article
Author list: CUNTZ J, QUILLEN D
Publication year: 1993
Volume number: 317
Issue number: 10
Start page: 917
End page: 922
Number of pages: 6
ISSN: 0764-4442
Languages: English-Great Britain (EN-GB)
Abstract
Generalizing a well-known notion due to Wodzicki we say that an algebra J is approximately H-unital if the complex (lim --> k C(n)(J(k)), b') is acyclic. We show that any exact sequence 0 --> J --> A --> A/J --> 0 where J is approximately H-unital induces a six-term exact sequence connecting the periodic cyclic cohomology groups of J, A and A/J. We further show that most algebras arising in applications are approximately H-unital. In particular this holds for the ideals IA and qA in the universal extension and in the universal split extension of A.
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