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A groupoid approach to C*-algebras
Jean Renault
- 01 Jan 1980
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About: The article was published on 01 Jan 1980. and is currently open access. The article focuses on the topics: Groupoid algebra & Double groupoid.
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Citations
Some remarks on $\mathrm{K}_0$ of noncommutative tori
TL;DR: This article constructed projective modules over a continuous field of C*-algebras whose fibres are noncommutative tori, using Rieffel's construction of projective module over higher dimensional non-commodity tori.
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AF inverse monoids and the structure of countable MV-algebras
Mark V. Lawson,Philip J. Scott +1 more
TL;DR: In this article, the authors define a class of inverse monoids having the property that their lattices of principal ideals naturally form an MV-algebra, and prove that every countable MV algebra can be co-ordinatized if it is isomorphic to one constructed in this way from a monoid.
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A general Banach–Stone type theorem and applications
TL;DR: In this paper, a general framework for disjointness relations on groups of functions is presented, which can be used for new applications related to groupoid algebras and to groups of circle-valued functions.
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Hausdorff Measures and KMS States
Marius Ionescu,Alex Kumjian +1 more
TL;DR: In this article, it was shown that the Hausdorff measure on a compact metric space gives rise to a KMS state on the C^{*}-algebra naturally associated to the pair $(X,T)$ such that the inverse temperature coincides with the Haudorff dimension.
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Finite symmetry group actions on substitution tiling C*-algebras
TL;DR: For a finite symmetry group G of an aperiodic substitution tiling system, this paper showed that the crossed product of the tiling C � -algebra A! by G has real rank zero, tracial rank one, a unique trace, and that order on its K-theory is determined by the trace.
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