$\mathrm C^*$-algebras of Boolean inverse monoids – traces and invariant means
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Bibliographic record
Abstract
To a Boolean inverse monoid S we associate a universal C*-algebra C^*_{B}(S) and show that it is equal to Exel's tight C*-algebra of S . We then show that any invariant mean on S (in the sense of Kudryavtseva, Lawson, Lenz and Resende) gives rise to a trace on C^*_{B}(S) , and vice-versa, under a condition on S equivalent to the underlying groupoid being Hausdorff. Under certain mild conditions, the space of traces of C^*_{B}(S) is shown to be isomorphic to the space of invariant means of S . We then use many known results about traces of C*-algebras to draw conclusions about invariant means on Boolean inverse monoids; in particular we quote a result of Blackadar to show that any metrizable Choquet simplex arises as the space of invariant means for some AF inverse monoid S .
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
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| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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