Generalized inductive limits and maximal stably finite quotients of C⁎-algebras

2021 ◽  
pp. 125692
Author(s):  
Hongliang Yao
Keyword(s):  
Inductive Limits ◽  
C Algebras ◽  
Finite Quotients ◽  
Stably Finite

scholarly journals Nuclear subalgebras of UHF C*-algebras

1986 ◽  
Vol 29 (1) ◽  
pp. 97-100 ◽  
Author(s):  
R. J. Archbold ◽  
Alexander Kumjian
Keyword(s):  
Tensor Product ◽  
Inductive Limit ◽  
Inductive Limits ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
The Family ◽  
Algebraic Tensor Product

A C*-algebra A is said to be approximately finite dimensional (AF) if it is the inductive limit of a sequence of finite dimensional C*-algebras(see [2], [5]). It is said to be nuclear if, for each C*-algebra B, there is a unique C*-norm on the *-algebraic tensor product A ⊗B [11]. Since finite dimensional C*-algebras are nuclear, and inductive limits of nuclear C*-algebras are nuclear [16];,every AF C*-algebra is nuclear. The family of nuclear C*-algebras is a large and well-behaved class (see [12]). The AF C*-algebras for a particularly tractable sub-class which has been completely classified in terms of the invariant K0 [7], [5].

C* -Algebras of Real Rank Zero Whose K0's are not Riesz Groups

1996 ◽  
Vol 39 (4) ◽  
pp. 429-437 ◽  
Author(s):  
K. R. Goodearl
Keyword(s):  
Real Rank ◽  
Riesz Decomposition Property ◽  
Real Rank Zero ◽  
Decomposition Property ◽  
Rank Zero ◽  
C Algebras ◽  
Finite Dimensional ◽  
Riesz Decomposition ◽  
Stably Finite ◽  
The Riesz Decomposition Property

AbstractExamples are constructed of stably finite, imitai, separable C* -algebras A of real rank zero such that the partially ordered abelian groups K0(A) do not satisfy the Riesz decomposition property. This contrasts with the result of Zhang that projections in C* -algebras of real rank zero satisfy Riesz decomposition. The construction method also produces a stably finite, unital, separable C* -algebra of real rank zero which has the same K-theory as an approximately finite dimensional C*-algebra, but is not itself approximately finite dimensional.

On a class of stably finite nuclear C*-algebras

1995 ◽  
Vol 22 (3) ◽  
pp. 339-351 ◽  
Author(s):  
Ghislain Vaillant
Keyword(s):  
C Algebras ◽  
Stably Finite

Rokhlin dimension of ℤm-actions on simple C∗-algebras

2017 ◽  
Vol 28 (07) ◽  
pp. 1750050 ◽  
Author(s):  
Hung-Chang Liao
Keyword(s):  
Large Class ◽  
C Algebras ◽  
Stably Finite

We study Rokhlin dimension of [Formula: see text]-actions on simple separable stably finite nuclear [Formula: see text]-algebras. We prove that under suitable assumptions, a strongly outer [Formula: see text]-action has finite Rokhlin dimension. This extends the known result for automorphisms. As an application, we show that for a large class of [Formula: see text]-algebras, the [Formula: see text]-Bernoulli action has finite Rokhlin dimension.

scholarly journals A Continuous Field of Projectionless C*-Algebras

2001 ◽  
Vol 53 (1) ◽  
pp. 51-72 ◽  
Author(s):  
Andrew Dean
Keyword(s):  
Continuous Functions ◽  
Unit Interval ◽  
Type I ◽  
Crossed Products ◽  
Inductive Limits ◽  
Direct Sums ◽  
Matrix Algebras ◽  
C Algebras ◽  
Finite Dimensional ◽  
Continuous Field

AbstractWe use some results about stable relations to show that some of the simple, stable, projectionless crossed products of O2 by considered by Kishimoto and Kumjian are inductive limits of type C*-algebras. The type I C*-algebras that arise are pullbacks of finite direct sums of matrix algebras over the continuous functions on the unit interval by finite dimensional C*-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.

Quasi*-algebras and generalized inductive limits of C*-algebras

2011 ◽  
Vol 202 (2) ◽  
pp. 165-190 ◽  
Author(s):  
Giorgia Bellomonte ◽  
Camillo Trapani
Keyword(s):  
Inductive Limits ◽  
C Algebras

scholarly journals On the Classification of Simple Stably Projectionless C*-Algebras

2002 ◽  
Vol 54 (1) ◽  
pp. 138-224 ◽  
Author(s):  
Shaloub Razak
Keyword(s):  
Building Blocks ◽  
Isomorphism Theorem ◽  
Inductive Limits ◽  
C Algebras ◽  
Distinguished Subset ◽  
K Theory

AbstractIt is shown that simple stably projectionless C*-algebras which are inductive limits of certain specified building blocks with trivial K-theory are classified by their cone of positive traces with distinguished subset. This is the first example of an isomorphism theorem verifying the conjecture of Elliott for a subclass of the stably projectionless algebras.

On Inductive Limits for Systems of C*-Algebras

2018 ◽  
Vol 62 (7) ◽  
pp. 68-73 ◽  
Author(s):  
R. N. Gumerov ◽  
E. V. Lipacheva ◽  
T. A. Grigoryan
Keyword(s):  
Inductive Limits ◽  
C Algebras

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.

Sign in / Sign up

Export Citation Format

Share Document