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- W1983410588 abstract "We consider linearly ordered, Archimedean dimension groups (G,G+,u) for which the group G/〈u〉 is torsion-free. It will be shown that if, in addition, G/〈u〉 is generated by a single element (i.e., G/〈u〉≅Z), then (G,G+,u) is isomorphic to (Z+τZ,(Z+τZ)∩R+,1) for some irrational number τ∈(0,1). This amounts to an extension of related results where dimension groups for which G/〈u〉 is torsion were considered. We will prove, in the case of the Fibonacci dimension group, that these results can be used to directly construct an equivalence relation groupoid whose C∗-algebra is the Fibonacci C∗-algebra." @default.
- W1983410588 created "2016-06-24" @default.
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- W1983410588 date "2009-12-01" @default.
- W1983410588 modified "2023-09-26" @default.
- W1983410588 title "Equivalence relation groupoids associated with certain linearly ordered dimension groups" @default.
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- W1983410588 doi "https://doi.org/10.1016/j.jmaa.2009.06.026" @default.
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