Strict comparison and Z-absorption of nuclear C*-algebras

By H. Matui, Yasuhiko Sato. 2011

154 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/558172a5ca391350ac56f2a43860d484aa691be0

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Citations in the corpus

Nuclear dimension of simple $$\mathrm {C}^*$$-algebras (2019, methodology): “The uniqueness ingredient (ii) was obtained in [3] under the same compactness assumption on the tracial extreme boundary of A.6 This uses a detailed analysis of the structure of relative commutants, building on Matui and Sato’s groundbreaking techniques for transferring structure between von Neumann”
Covering Dimension of C*-Algebras and 2-Coloured Classification (2015, background): “, its extreme boundary ∂eT (A) is compact) and ∂eT (A) has finite covering dimension [31, 53, 60] (this extends the innovative work [38] which handles the case of finitely many extremal traces).”
Dimension, comparison, and almost finiteness (2017, background): “Matui and Sato proved (iii)⇒(ii) when the set of extremal tracial states is finite [28], and this was later generalized to the case where the extreme traces form a nonempty compact set with finite covering dimension [22, 39, 47].”
Classifying crossed product C*-algebras (2013, methodology): “Our version is less general since we need to assume ﬁnite nuclear dimension; on the other hand, the proof is substantially simpler since it avoids the von Neumann algebra techniques pivotal for [21] (see also [20]).”
Rokhlin Dimension and C*-Dynamics (2012, methodology): “Their argument is based on the techniques developed in [18].”
Almost Finiteness and the Small Boundary Property (2018, methodology): “This commingling of the measure-theoretic with the topological is very much line with the kind of C∗-application of von Neumann algebra technology that was pioneered by Matui and Sato in their groundbreaking work on the Toms–Winter conjecture [31, 32].”
Nuclear dimension and $$\mathcal Z$$Z-stability (2014, background): “Moreover, the implications (i) =⇒ (ii) and (ii) =⇒ (iii) have been established in general by the third named author [42, 44] (see [34] for an extension to the stably projectionless case) and Rørdam [29] respectively; recent progress of Matui and the first named author [23] establishes (iii) =⇒ (ii) ”
Subalgebras of simple AF-algebras (2018, background): “The trace-kernel extension has been extensively studied in connection with the TomsWinter conjecture (with a modified definition when B has more than one trace); see [5, 44, 54, 55, 75, 76, 83] for example.”
Tracially Z-absorbing C*-algebras (2012, methodology): “In section 5 we define a projectionless version of the tracial Rokhlin property for finite group actions and we show that tracial Z-absorption passes to crossed products under such actions.”