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RATIONAL $\boldsymbol {K}$-STABILITY OF CONTINUOUS $\boldsymbol {C(X)}$-ALGEBRAS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  10 May 2022

APURVA SETH  and
PRAHLAD VAIDYANATHAN
APURVA SETH
Affiliation:
Department of Mathematics, IISER Bhopal, Bhopal ByPass Road, Bhauri, Bhopal 462066, Madhya Pradesh, India e-mail: apurva17@iiserb.ac.in
PRAHLAD VAIDYANATHAN*
Affiliation:
Department of Mathematics, IISER Bhopal, Bhopal ByPass Road, Bhauri, Bhopal 462066, Madhya Pradesh, India
*
e-mail: prahlad@iiserb.ac.in
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Abstract

We show that the properties of being rationally K-stable passes from the fibres of a continuous $C(X)$-algebra to the ambient algebra, under the assumption that the underlying space X is compact, metrizable, and of finite covering dimension. As an application, we show that a crossed product C*-algebra is (rationally) K-stable provided the underlying C*-algebra is (rationally) K-stable, and the action has finite Rokhlin dimension with commuting towers.

Keywords

nonstable K-theoryC*-algebras

MSC classification

Primary: 46L85: Noncommutative topology
Secondary: 46L80: $K$-theory and operator algebras (including cyclic theory)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 115 , Issue 1 , August 2023 , pp. 119 - 144
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Robert Yuncken

The first named author is supported by UGC Junior Research Fellowship No. 1229, and the second named author was partially supported by the SERB (Grant No. MTR/2020/000385).

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