Rational $K$-Stability of Continuous $C(X)$-Algebras

Apurva Seth; Prahlad Vaidyanathan

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arXiv · 2102.13529

Rational $K$-Stability of Continuous $C(X)$-Algebras

Apurva Seth·Prahlad Vaidyanathan

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Abstract

We show that the property of being rationally $K$-stable passes from the fibers 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.

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BibTeX RIS

Apurva Seth, Prahlad Vaidyanathan. 2021-02-26. Rational $K$-Stability of Continuous $C(X)$-Algebras. https://arxiv.org/abs/2102.13529

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