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Radius of comparison and mean topological dimension:
$\mathbb Z^d$-actions
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 76 / Issue 4 / August 2024
- Published online by Cambridge University Press:
- 19 June 2023, pp. 1240-1266
- Print publication:
- August 2024
-
- Article
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- You have access
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Consider a minimal-free topological dynamical system
$(X, \mathbb Z^d)$. It is shown that the radius of comparison of the crossed product C*-algebra 
$\mathrm {C}(X) \rtimes \mathbb Z^d$ is at most half the mean topological dimension of 
$(X, \mathbb Z^d)$. As a consequence, the C*-algebra 
$\mathrm {C}(X) \rtimes \mathbb Z^d$ is classified by the Elliott invariant if the mean dimension of 
$(X, \mathbb Z^d)$ is zero.
