Tracially AF *-algebras

By Huaxin Lin. 2000

91 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fbf589856af8bc6cb8c7ad1069dd9626bcd353b7

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In Algebra and Number Theory

In Computational Theory and Mathematics

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Citations in the corpus

A classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras, I: $C^*$-algebras with generalized tracial rank one. (2018, background): “2 of [59], C2 has real rank zero and projections in B lifts to a projection in C2.”
Crossed products by minimal homeomorphisms (2004, background): “3, and [20], Lemma 2.”
Simple nuclear C∗-algebras of tracial topological rank one (2004, background): “ras with tracial rank zero. For example it is known (see for example Theorem 1.15 of GPS [10]) that C(X) ⋊αZ is a AT-algebra of real rank zero if X is the Cantor set. It follows (see EG [7] and Lntaf [29]) that they have tracial rank zero. More recently it is shown by Q. Lin and N.C. Phillips ( LqP ”
Subalgebras of simple AF-algebras (2018, methodology): “The proof is motivated by the classical classification results for tracially AF-algebras in [17] and [48], but it avoids making any use of the internal structure of the domain C∗-algebra and makes no use of inductive limit models such as the AH-algebras used in [48].”
On the Classification of Simple Z‐Stable C*‐Algebras with Real Rank Zero and Finite Decomposition Rank (2005, background): “he notion of tracially AF C∗-algebras and provide an alternative characterization of when a simple unital C∗-algebra with Blackadar’s second fundamental comparability property is tracially AF. 3.1 In [8], Lin introduced the notion of tracially AF algebras (or, equivalently, C∗- algebras of tracial r”
On tracial approximation (2008, background): “Instead of assuming inductive limit structure, he started with a certain abstract approximation property, and showed that C*-algebras with this abstract approximation property and certain additional properties are AH-algebras without dimension growth [18, 20,21,23].”
Crossed Products of the Cantor Set by Free Minimal Actions of ℤd (2002, unknown): “1 of [30]?”
Dimension, comparison, and almost finiteness (2017, background): “which has its roots in work of Gong [9] and Popa [38] and was formalized and applied by Lin in his seminal work of the 1990s as a way to circumvent inductive limit hypotheses in the stably ﬁnite case [26, 27, 28], continues to do much of the technical legwork in classiﬁcation. The simple unital proj”
On the classification of simple amenable C*-algebras with finite decomposition rank (2015, background): “ the map C 1 → Cis an embedding, it follows that the map C 1 → Ais also an embedding. By (2.12), (2.13), and (2.3), one then has kφ∗ ◦ψ∗(fˆ)− fˆk∞ <ε, f∈ F, as desired. Recall that Deﬁnition 2.11 ([15], [8]). Let S be a class of unital C*-algebras. A C*-algebra Ais said to be tracially approximat”
Decomposition rank of UHF-absorbing c* -algebras (2013, methodology): “This enables us to remove the technical condition from H. Lin’s result [16, Corollary 5.10] for nuclear C∗-algebras, and to provide a partial answer to his conjecture mentioned in the introduction of [16]. As an application, we construct a counter-example to the Powers-Sakai conjecture. In Section 7”