Abstract
Abstract
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.
Publisher
Cambridge University Press (CUP)
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