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On the Radius of Comparison of a Commutative C*-algebra

Published online by Cambridge University Press:  20 November 2018

George A. Elliott  and
Zhuang Niu
George A. Elliott
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4 e-mail: elliott@math.toronto.edu
Zhuang Niu
Affiliation:
Department of Mathematics, University of Wyoming, Laramie, Wyoming, USA 82071 e-mail: zniu@mun.ca
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Abstract.

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Let $X$ be a compact metric space. A lower bound for the radius of comparison of the ${{\text{C}}^{*}}$-algebra $\text{C}\left( X \right)$ is given in terms of ${{\dim}_{\mathbb{Q}}}\,X$, where ${{\dim}_{\mathbb{Q}}}\,X$ is the cohomological dimension with rational coefficients. If ${{\dim}_{\mathbb{Q}}}\,X\,=\,\dim\,X\,=\,d$, then the radius of comparison of the ${{\text{C}}^{*}}$-algebra $C\left( X \right)$ is $\max \left\{ 0,\,\left( d\,-\,1 \right)/\,2\,-\,1 \right\}$ if $d$ is odd, and must be either ${d}/{2}\;\,-\,1$ or ${d}/{2}\;\,-\,2$ if $d$ is even (the possibility ${d}/{2}\;\,-\,1$ does occur, but we do not know if the possibility ${d}/{2}\;\,-\,2$ can also occur).

Keywords

46L80Cuntz semigroupcomparison radiuscohomology dimensioncovering dimension
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 4 , 01 December 2013 , pp. 737 - 744
Copyright
Copyright © Canadian Mathematical Society 2013

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