On the classification of 𝐶*-algebras of real rank zero: inductive limits of matrix algebras over non-Hausdorff graphs

1995 ◽  
Vol 114 (547) ◽  
pp. 0-0 ◽  
Author(s):  
Hongbing Su
Keyword(s):  
Real Rank ◽  
Inductive Limits ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Matrix Algebras

The classification of certain ASH C*-algebras of real rank zero

2020 ◽  
pp. 1-20
Author(s):  
Qingnan An ◽  
George A. Elliott ◽  
Zhiqiang Li ◽  
Zhichao Liu
Keyword(s):  
Real Rank ◽  
Inductive Limits ◽  
Real Rank Zero ◽  
Direct Sums ◽  
Rank Zero ◽  
The Real ◽  
C Algebras ◽  
Generalized Dimension ◽  
Theoretic Classification

In this paper, using ordered total K-theory, we give a K-theoretic classification for the real rank zero inductive limits of direct sums of generalized dimension drop interval algebras.

scholarly journals Inductive Limits of K-theoretic Complexes with Torsion Coefficients

2007 ◽  
Vol 1 (1) ◽  
pp. 145-168
Author(s):  
Søren Eilers ◽  
Andrew S. Toms
Keyword(s):  
Real Rank ◽  
Inductive Limits ◽  
Real Rank Zero ◽  
Rank Zero ◽  
K Theory

AbstractWe present the first range result for the total K-theory of C*-algebras. This invariant has been used successfully to classify certain separable, nuclear C*-algebras of real rank zero. Our results complete the classification of the so-called AD algebras of real rank zero.

scholarly journals On the classification of C*-algebras of real rank zero, III: The infinite case

1998 ◽  
pp. 11-72 ◽  
Author(s):  
Ola Bratteli ◽  
George Elliott ◽  
David Evans ◽  
Akitaka Kishimoto
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras ◽  
Infinite Case

Homomorphisms From C(X) Into C*-Algebras

1997 ◽  
Vol 49 (5) ◽  
pp. 963-1009 ◽  
Author(s):  
Huaxin Lin
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
Countable Rank ◽  
Rank One ◽  
Dimensional Range

AbstractLet A be a simple C*-algebra with real rank zero, stable rank one and weakly unperforated K0(A) of countable rank. We show that a monomorphism Φ: C(S2) → A can be approximated pointwise by homomorphisms from C(S2) into A with finite dimensional range if and only if certain index vanishes. In particular,we show that every homomorphism ϕ from C(S2) into a UHF-algebra can be approximated pointwise by homomorphisms from C(S2) into the UHF-algebra with finite dimensional range.As an application, we show that if A is a simple C*-algebra of real rank zero and is an inductive limit of matrices over C(S2) then A is an AF-algebra. Similar results for tori are also obtained. Classification of Hom (C(X), A) for lower dimensional spaces is also studied.

scholarly journals Classification of real rank zero, purely infinite C⁎-algebras with at most four primitive ideals

2016 ◽  
Vol 271 (7) ◽  
pp. 1921-1947
Author(s):  
Sara E. Arklint ◽  
Gunnar Restorff ◽  
Efren Ruiz
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras ◽  
Primitive Ideals

scholarly journals A decomposition theorem for real rank zero inductive limits of 1-dimensional non-commutative CW complexes

2019 ◽  
Vol 11 (01) ◽  
pp. 181-204
Author(s):  
Zhichao Liu
Keyword(s):  
Inductive Limit ◽  
Decomposition Theorem ◽  
Building Blocks ◽  
Classification Theorem ◽  
Real Rank ◽  
Inductive Limits ◽  
Real Rank Zero ◽  
Rank Zero ◽  
The Real ◽  
Cw Complexes

In this paper, we consider the real rank zero [Formula: see text]-algebras which can be written as an inductive limit of the Elliott–Thomsen building blocks and prove a decomposition result for the connecting homomorphisms; this technique will be used in the classification theorem.

scholarly journals The crossed product of a UHF algebra by a shift

1993 ◽  
Vol 13 (4) ◽  
pp. 615-626 ◽  
Author(s):  
Ola Bratteli ◽  
Erling Størmer ◽  
Akitaka Kishimoto ◽  
Mikael Rørdam
Keyword(s):  
Inductive Limit ◽  
Crossed Product ◽  
Cuntz Algebra ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Full Matrix ◽  
Matrix Algebras ◽  
Car Algebra ◽  
Homogeneous Algebras

AbstractWe prove that the crossed product of the CAR algebra M2∞ by the shift is an inductive limit of homogeneous algebras over the circle with fibres full matrix algebras. As a consequence the crossed product has real rank zero, and where is the Cuntz algebra of order 2.

Approximate homogeneity is not a local property

1999 ◽  
Vol 1999 (507) ◽  
pp. 1-13 ◽  
Author(s):  
Marius Dădărlat ◽  
Søren Eilers
Keyword(s):  
Local Property ◽  
List Type ◽  
Real Rank ◽  
Inductive Limits ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Splitting Property ◽  
Locally Homogeneous

Abstract It is shown that the AH algebras satisfy a certain splitting property at the level of K-theory with torsion coefficients. The splitting property is used to prove the following: There are locally homogeneous C*-algebras which are not AH algebras.The class of AH algebras is not closed under countable inductive limits.There are real rank zero split quasidiagonal extensions of AH algebras which are not AH algebras.

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