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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Extensions relative to a $ {\rm II}\sb{\infty }$-factor


Author: Sung Je Cho
Journal: Proc. Amer. Math. Soc. 74 (1979), 109-112
MSC: Primary 46L99
DOI: https://doi.org/10.1090/S0002-9939-1979-0521882-8
MathSciNet review: 521882
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Abstract: It will be shown that the equivalence classes of $ {C^\ast}$-algebra extensions of $ C(X)$ relative to a $ {\text{II}_\infty }$-factor and $ \operatorname{Hom}({\tilde K^1}(X),{\mathbf{R}})$ are isomorphic. This provides a proof for the result of Brown, Douglas and Fillmore [5] on the isomorphism between the former group and $ \operatorname{Hom}(\tilde K_{{\text{II}}}^1(X),{\mathbf{R}})$.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0521882-8
Keywords: $ {\text{II}_\infty }$-factor, $ {C^\ast}$-algebra extension, compact operators, Calkin algebra, Steenrod homology
Article copyright: © Copyright 1979 American Mathematical Society

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