scholarly journals EXACTNESS OF CUNTZ–PIMSNER C*-ALGEBRAS

2001 ◽  
Vol 44 (2) ◽  
pp. 425-444 ◽  
Author(s):  
Kenneth J. Dykema ◽  
Dimitri Shlyakhtenko
Keyword(s):  
Topological Entropy ◽  
Subject Classification ◽  
Primary 46L08 ◽  
Free Products ◽  
C Algebra ◽  
C Algebras ◽  
Amalgamated Free Products ◽  
Finite Dimensional

AbstractLet $H$ be a full Hilbert bimodule over a $C^*$-algebra $A$. We show that the Cuntz–Pimsner algebra associated to $H$ is exact if and only if $A$ is exact. Using this result, we give alternative proofs for exactness of reduced amalgamated free products of exact $C^*$-algebras. In the case in which $A$ is a finite-dimensional $C^*$-algebra, we also show that the Brown–Voiculescu topological entropy of Bogljubov automorphisms of the Cuntz–Pimsner algebra associated to an $A,A$ Hilbert bimodule is zero.AMS 2000 Mathematics subject classification: Primary 46L08. Secondary 46L09; 46L54

scholarly journals Conditions for primitivity of unital amalgamated full free products of finite-dimensional C*-algebras

2014 ◽  
Vol 25 (09) ◽  
pp. 1450086
Author(s):  
Francisco Torres-Ayala
Keyword(s):  
Free Products ◽  
C Algebra ◽  
C Algebras ◽  
Finite Dimensional ◽  
Trivial Center

We consider amalgamated unital full free products of the form A1*D A2, where A1, A2 and D are finite-dimensional C*-algebras and there are faithful traces on A1 and A2 whose restrictions to D agree. We provide several conditions on the matrices of partial multiplicities of the inclusions D ↪ A1 and D ↪ A2 that guarantee that the C*-algebra A1*D A2 is primitive. If the ranks of the matrices of partial multiplicities are one or all entries are 0 or ≥ 2, we prove that the algebra A1*D A2 is primitive if and only if it has a trivial center.

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].

On Unital Full Amalgamated Free Products of Quasidiagonal C*-Algebras

2016 ◽  
Vol 50 (1) ◽  
pp. 39-47
Author(s):  
Qihui Li ◽  
Don Hadwin ◽  
Jiankui Li ◽  
Xiujuan Ma ◽  
Junhao Shen
Keyword(s):  
Free Products ◽  
C Algebras ◽  
Amalgamated Free Products

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.

Simple ${\bi C}^*$-algebras arising from ${\beta}$-expansion of real numbers

1998 ◽  
Vol 18 (4) ◽  
pp. 937-962 ◽  
Author(s):  
YOSHIKAZU KATAYAMA ◽  
KENGO MATSUMOTO ◽  
YASUO WATATANI
Keyword(s):  
Real Number ◽  
Topological Entropy ◽  
Symbolic Dynamics ◽  
Partial Isometry ◽  
Inverse Temperature ◽  
Real Numbers ◽  
Gauge Action ◽  
C Algebra ◽  
C Algebras ◽  
Kms State

Given a real number $\beta > 1$, we construct a simple purely infinite $C^*$-algebra ${\cal O}_{\beta}$ as a $C^*$-algebra arising from the $\beta$-subshift in the symbolic dynamics. The $C^*$-algebras $\{{\cal O}_{\beta} \}_{1<\beta \in {\Bbb R}}$ interpolate between the Cuntz algebras $\{{\cal O}_n\}_{1 < n \in {\Bbb N}}$. The K-groups for the $C^*$-algebras ${\cal O}_{\beta}$, $1 < \beta \in {\Bbb R}$, are computed so that they are completely classified up to isomorphism. We prove that the KMS-state for the gauge action on ${\cal O}_{\beta}$ is unique at the inverse temperature $\log \beta$, which is the topological entropy for the $\beta$-shift. Moreover, ${\cal O}_{\beta}$ is realized to be a universal $C^*$-algebra generated by $n-1=[\beta]$ isometries and one partial isometry with mutually orthogonal ranges and a certain relation coming from the sequence of $\beta$-expansion of $1$.

scholarly journals C*-ALGEBRAS THAT ARE ISOMORPHIC AFTER TENSORING AND FULL PROJECTIONS

2004 ◽  
Vol 47 (3) ◽  
pp. 659-668
Author(s):  
Kazunori Kodaka
Keyword(s):  
Matrix Algebra ◽  
Subject Classification ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Primary 46L05 ◽  
C Algebra ◽  
C Algebras ◽  
Necessary And Sufficient

AbstractLet $A$ be a unital $C^*$-algebra and for each $n\in\mathbb{N}$ let $M_n$ be the $n\times n$ matrix algebra over $\mathbb{C}$. In this paper we shall give a necessary and sufficient condition that there is a unital $C^*$-algebra $B$ satisfying $A\not\cong B$ but for which $A\otimes M_n\cong B\otimes M_n$ for some $n\in\mathbb{N}\setminus\{1\}$. Also, we shall give some examples of unital $C^*$-algebras satisfying the above property.AMS 2000 Mathematics subject classification: Primary 46L05

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