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Tracial weights on topological graph algebras
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 44 / Issue 12 / December 2024
- Published online by Cambridge University Press:
- 05 March 2024, pp. 3428-3454
- Print publication:
- December 2024
-
- Article
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We describe two kinds of regular invariant measures on the boundary path space
$\partial E$ of a second countable topological graph E, which allows us to describe all extremal tracial weights on 
$C^{*}(E)$ which are not gauge-invariant. Using this description, we prove that all tracial weights on the C
$^{*}$-algebra 
$C^{*}(E)$ of a second countable topological graph E are gauge-invariant when E is free. This in particular implies that all tracial weights on 
$C^{*}(E)$ are gauge-invariant when 
$C^{*}(E)$ is simple and separable.
