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.

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 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.

scholarly journals CERTAIN APERIODIC AUTOMORPHISMS OF UNITAL SIMPLE PROJECTIONLESS C*-ALGEBRAS

2009 ◽  
Vol 20 (10) ◽  
pp. 1233-1261 ◽  
Author(s):  
YASUHIKO SATO
Keyword(s):  
Inductive Limit ◽  
Crossed Products ◽  
Inductive Limits ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebra ◽  
Tracial State ◽  
C Algebras ◽  
Cyclic Groups ◽  
Unital Simple

Let G be an inductive limit of finite cyclic groups, and A be a unital simple projectionless C*-algebra with K1(A) ≅ G and a unique tracial state, as constructed based on dimension drop algebras by Jiang and Su. First, we show that any two aperiodic elements in Aut (A)/ WInn (A) are conjugate, where WInn (A) means the subgroup of Aut (A) consisting of automorphisms which are inner in the tracial representation.In the second part of this paper, we consider a class of unital simple C*-algebras with a unique tracial state which contains the class of unital simple A𝕋-algebras of real rank zero with a unique tracial state. This class is closed under inductive limits and crossed products by actions of ℤ with the Rohlin property. Let A be a TAF-algebra in this class. We show that for any automorphism α of A there exists an automorphism ᾶ of A with the Rohlin property such that ᾶ and α are asymptotically unitarily equivalent. For the proof we use an aperiodic automorphism of the Jiang-Su algebra.

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.

EXTENSIONS BY C*-ALGEBRAS WITH REAL RANK ZERO

1993 ◽  
Vol 04 (02) ◽  
pp. 231-252 ◽  
Author(s):  
HUAXIN LIN
Keyword(s):  
Unit Circle ◽  
Compact Subset ◽  
Real Line ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
The Real ◽  
C Algebra ◽  
C Algebras ◽  
Essential Extensions

We show that all trivial (unital and essential) extensions of C (X) by a σ-unital purely infinite simple C*-algebra A with K1(A) = 0 are unitarily equivalent, provided that X is homeomorphic to a compact subset of the real line or the unit circle. Therefore all (unital and essential) extensions of such can be completely determined by Ext(B, A). An invariant is introduced to classify all such trivial (unital and essential) extensions of C (X) by a σ-unital C*-algebra A with the properties that RR (M (A)) = 0 and C (A) is simple.

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