The Tracial Topological Rank of C*‐Algebras

By Huaxin Lin. 2001

180 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/57072f9624be3b7cbe562822a8cf4386935927e8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Covering dimension for nuclear C∗-algebras (2001, background): “gebra A, rrA≤ cprA. 5.2 Tracial rank For recent development in classiﬁcation of nuclear C∗-algebras tracially AFand tracially AIalgebras (introduced by Lin in [Li1]) have been of certain interest. In [Li2], Lin has given a notion of covering dimension closely related to these concepts. 5.2.1 Denote ”
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].”
The tracial Rokhlin property for actions of finite groups on C*-algebras (2006, background): “9 of [15], with (3) as it stands, the resulting condition implies that A has stable rank one.”
Freeness of actions of finite groups on C*-algebras (2009, background): “1 of [37]; the equivalence is Theorem 7.”
Regularity properties in the classification program for separable amenable C*-algebras (2007, background): “Lin in [37] introduced the concept of tracial topological rank for C-algebras.”
Classification of homomorphisms and dynamical systems (2004, background): “Since T R(A) = 0, by Theorem 7.1 of [ 37 ], A has real rank zero, stable rank one and weakly unperforated K0(A).”
On the Classification of Simple Z‐Stable C*‐Algebras with Real Rank Zero and Finite Decomposition Rank (2005, background): “3.2 Recall that a unital C ∗-algebra A is said to have Blackadar’s second fundamental comparability property, if, whenever p and q are projections in A such that τ(p) 10 ], Corollary 6.15, Lin provided a characterization of when a C ∗-algebra with real rank zero and comparability is tracially AF. F”
Every simple higher dimensional noncommutative torus is an AT algebra (2006, background): “13 of [20] show that K0(A) is weakly unperforated and satisfies the Riesz interpolation property (equivalently, by Proposition 2.”
The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ) (2006, background): “8 of [40]), it suffices to find a group isomorphism f as above such that (τ2, 1−θ)∗ ◦ f = (τ2,θ)∗ and f([1]) = [1].”
Classification of simple C*-algebras of tracial topological rank zero (2000, background): “In [Ln7] and [ Ln10 ], we introduced the notion of tracial topological rank.”
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”
Sequentially split ∗-homomorphisms between C*-algebras (2015, background): “ferred to [7] and the references therein, featuring an excellent overview of the current state-of-the-art in its introduction. Another kind of regularity properties includes having ﬁnite tracial rank [38] or having generalized tracial rank at most one [24]. The latter class of C∗-algebras is an impo”