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Central sequences of C*algebras and tensorial absorption of the JiangSu algebra
 J. Reine Angew. Math.(2012
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OMITTING TYPES AND AF ALGEBRAS
"... The model theory of metric structures ([3]) was successfully applied to analyze ultrapowers of C*algebras in [13] and [12]. Since important classes of separable C*algebras, such as UHF, AF, or nuclear algebras, are not elementary (i.e., not characterized by their theory—see [12, §6.1]), for a mome ..."
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The model theory of metric structures ([3]) was successfully applied to analyze ultrapowers of C*algebras in [13] and [12]. Since important classes of separable C*algebras, such as UHF, AF, or nuclear algebras, are not elementary (i.e., not characterized by their theory—see [12, §6.1]), for a moment it seemed that model theoretic methods do not apply to these classes of C*algebras. We prove results suggesting that this is not the case. Many of the prominent problems in the modern theory of C*algebras are concerned with the extent of the class of nuclear C*algebras. We have the bootstrap class problem (see [5, IV3.1.16]), the question of whether all nuclear C*algebras satisfy the Universal Coefficient Theorem, UCT, (see [21, §2.4]), and the Toms—Winter conjecture (to the effect that the three regularity properties of nuclear C*algebras discussed in [9] are equivalent; see [23]). If one could characterize classes of algebras in question—such as nuclear algebras, algebras with finite nuclear dimension, or algebras with finite decomposition rank—as algebras that omit certain sets of types (see
Unitary equivalence of automorphisms of separable C*algebras
 Adv. Math
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The Rokhlin property for automorphisms on simple C¤algebras, Operator theory, operator algebras, and applications
, 2006
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Finite group actions on certain stably projectionless C∗algebras with the Rokhlin property
, 1308
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Finite symmetry group actions on substitution tiling C*algebras. arXiv:1207.6301
, 2012
"... For a finite symmetry group G of an aperiodic substitution tiling system (P, ω), we show that the crossed product of the tiling C*algebra Aω by G has real rank zero, tracial rank one, a unique trace, and that order on its Ktheory is determined by the trace. We also show that the action of G on Aω ..."
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For a finite symmetry group G of an aperiodic substitution tiling system (P, ω), we show that the crossed product of the tiling C*algebra Aω by G has real rank zero, tracial rank one, a unique trace, and that order on its Ktheory is determined by the trace. We also show that the action of G on Aω satisfies the weak Rokhlin property, and that it also satisfies the tracial Rokhlin property provided that Aω has tracial rank zero. In the course of proving the latter we show that Aω is finitely generated. We also provide a link between Aω and the AF algebra Connes associated to the Penrose tilings. 1