Classification of Homomorphisms from C (X) to Simple C*-Algebras of Real Rank Zero

2000 ◽  
Vol 16 (2) ◽  
pp. 181-206 ◽  
Author(s):  
Guihua Gong ◽  
Huaxin Lin
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras

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

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.

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

On the Classification of C ∗ -Algebras of Real Rank Zero, II

1996 ◽  
Vol 144 (3) ◽  
pp. 497 ◽  
Author(s):  
George A. Elliott ◽  
Guihua Gong
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras

scholarly journals FILTRATED K-THEORY FOR REAL RANK ZERO C*-ALGEBRAS

2012 ◽  
Vol 23 (08) ◽  
pp. 1250078 ◽  
Author(s):  
SARA ARKLINT ◽  
GUNNAR RESTORFF ◽  
EFREN RUIZ
Keyword(s):  
Primitive Ideal ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras ◽  
K Theory

The smallest primitive ideal spaces for which there exist counterexamples to the classification of non-simple, purely infinite, nuclear, separable C*-algebras using filtrated K-theory, are four-point spaces. In this article, we therefore restrict to real rank zero C*-algebras with four-point primitive ideal spaces. Up to homeomorphism, there are ten different connected T0-spaces with exactly four points. We show that filtrated K-theory classifies real rank zero, tight, stable, purely infinite, nuclear, separable C*-algebras that satisfy that all simple subquotients are in the bootstrap class for eight out of ten of these spaces.

Sign in / Sign up

Export Citation Format

Share Document