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.

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 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 Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras

2014 ◽  
Vol 14 (3) ◽  
pp. 570-613 ◽  
Author(s):  
Sara E. Arklint ◽  
Rasmus Bentmann ◽  
Takeshi Katsura
Keyword(s):  
Primitive Ideal ◽  
Ideal Space ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
K Theory

AbstractWe show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C*-algebras with certain primitive ideal spaces—including the infinitely many so-called accordion spaces for which filtered K-theory is known to be a complete invariant. As a consequence, we give a characterization of purely infinite Cuntz–Krieger algebras whose primitive ideal space is an accordion space.

Linear Maps on C*-Algebras Preserving the Set of Operators that are Invertible in

2011 ◽  
Vol 54 (1) ◽  
pp. 141-146
Author(s):  
Sang Og Kim ◽  
Choonkil Park
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Calkin Algebra ◽  
C Algebras ◽  
Linear Maps

AbstractFor C*-algebras of real rank zero, we describe linear maps ϕ on that are surjective up to ideals , and π(A) is invertible in if and only if π(ϕ(A)) is invertible in , where A ∈ and π : → is the quotient map. We also consider similar linear maps preserving zero products on the Calkin algebra.

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