Abstract:
We consider the C *-algebra, A T , constructed from a substitution tiling system which is primitive, aperiodic and satisfies the finite pattern condition. Such a C *-algebra has a unique trace. We show that this trace completely determines the order structure on the group K 0(A T ); a non-zero element in K 0(A T ) is positive if and only if its image under the map induced from the trace is positive.
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Received: 12 August 1999 / Accepted: 2 May 2000
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Putnam, I. The Ordered K-Theory of C/*-Algebras¶Associated with Substitution Tilings. Commun. Math. Phys. 214, 593–605 (2000). https://doi.org/10.1007/s002200000278
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DOI: https://doi.org/10.1007/s002200000278