scholarly journals FRAÏSSÉ LIMITS OF C*-ALGEBRAS

2016 ◽  
Vol 81 (2) ◽  
pp. 755-773 ◽  
Author(s):  
CHRISTOPHER J. EAGLE ◽  
ILIJAS FARAH ◽  
BRADD HART ◽  
BORIS KADETS ◽  
VLADYSLAV KALASHNYK ◽  
...  
Keyword(s):  
Full Matrix ◽  
Matrix Algebras ◽  
C Algebras ◽  
Af Algebras

AbstractWe realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II1 factor as Fraïssé limits of suitable classes of structures. Moreover by means of Fraïssé theory we provide new examples of AF algebras with strong homogeneity properties. As a consequence of our analysis we deduce Ramsey-theoretic results about the class of full-matrix algebras.

scholarly journals THE UNITAL EXT-GROUPS AND CLASSIFICATION OF C*-ALGEBRAS

2019 ◽  
Vol 62 (1) ◽  
pp. 201-231 ◽  
Author(s):  
JAMES GABE ◽  
EFREN RUIZ
Keyword(s):  
Weak Version ◽  
C Algebras ◽  
Ext Groups ◽  
Theoretic Classification ◽  
Invertible Elements ◽  
Af Algebras

AbstractThe semigroups of unital extensions of separable C*-algebras come in two flavours: a strong and a weak version. By the unital Ext-groups, we mean the groups of invertible elements in these semigroups. We use the unital Ext-groups to obtain K-theoretic classification of both unital and non-unital extensions of C*-algebras, and in particular we obtain a complete K-theoretic classification of full extensions of UCT Kirchberg algebras by stable AF algebras.

scholarly journals HOMOGENEITY OF THE PURE STATE SPACE FOR SEPARABLE C*-ALGEBRAS

2001 ◽  
Vol 12 (07) ◽  
pp. 813-845 ◽  
Author(s):  
HAJIME FUTAMURA ◽  
NOBUHIRO KATAOKA ◽  
AKITAKA KISHIMOTO
Keyword(s):  
Automorphism Group ◽  
State Space ◽  
Large Class ◽  
Pure State ◽  
C Algebras ◽  
Inner Automorphisms ◽  
Af Algebras

We prove that the pure state space is homogeneous under the action of the automorphism group (or a certain smaller group of approximately inner automorphisms) for a fairly large class of simple separable nuclear C*-algebras, including the approximately homogeneous C*-algebras and the class of purely infinite C*-algebras which has been recently classified by Kirchberg and Phillips. This extends the known results for UHF algebras and AF algebras by Powers and Bratteli.

UHF FLOWS AND COCYCLES

2012 ◽  
Vol 23 (01) ◽  
pp. 1250018
Author(s):  
A. KISHIMOTO
Keyword(s):  
Explicit Construction ◽  
Inductive Limits ◽  
Full Matrix ◽  
Matrix Algebras

UHF flows are the flows obtained as inductive limits of flows on full matrix algebras. We will revisit universal UHF flows and give an explicit construction of such flows on a UHF algebra Mk∞ for any k and also present a characterization of such flows. Those flows are UHF flows whose cocycle perturbations are almost conjugate to themselves.

scholarly journals MORPHISMS OF SIMPLE TRACIALLY AF ALGEBRAS

2004 ◽  
Vol 15 (09) ◽  
pp. 919-957 ◽  
Author(s):  
MARIUS DADARLAT
Keyword(s):  
Existence And Uniqueness ◽  
Residually Finite ◽  
C Algebras ◽  
Finite Dimensional ◽  
K Theory ◽  
Inner Automorphisms ◽  
Af Algebras ◽  
Universal Coefficient Theorem

Let A, B be separable simple unital tracially AF C*-algebras. Assuming that A is exact and satisfies the Universal Coefficient Theorem (UCT) in KK-theory, we prove the existence, and uniqueness modulo approximately inner automorphisms, of nuclear *-homomorphisms from A to B with prescribed K-theory data. This implies the AF-embeddability of separable exact residually finite-dimensional C*-algebras satisfying the UCT and reproves Huaxin Lin's theorem on the classification of nuclear tracially AF C*-algebras.

Computing Explicit Isomorphisms with Full Matrix Algebras over $$\mathbb {F}_q(x)$$ F q ( x )

2017 ◽  
Vol 18 (2) ◽  
pp. 381-397 ◽  
Author(s):  
Gábor Ivanyos ◽  
Péter Kutas ◽  
Lajos Rónyai
Keyword(s):  
Full Matrix ◽  
Matrix Algebras

scholarly journals Subalgebras of C*-algebras and von Neumann algebras

1984 ◽  
Vol 25 (1) ◽  
pp. 19-25 ◽  
Author(s):  
Charles A. Akemann
Keyword(s):  
Recent Work ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Weierstrass Theorem ◽  
Von Neumann ◽  
Matrix Algebras ◽  
C Algebras ◽  
Weakly Closed

Recent work [2, 6] on subalgebras of matrix algebras leads naturally to the following situation. Let A be a C*-subalgebra of the C*-algebra B andM be a weakly closed *-subalgebra of the von Neumann algebra N. Consider the following Conditions.Condition 1. For every b≠ 0 in B there exists a ∈ A such that O≠ab ∈ A.Condition 2. For every b∈B there exists a ≠ 0 in A such that ab ∈ A.If we replace A by M and B by N in Conditions 1 and 2 we get von Neumann algebra versions which we shall call Condition 1'and Condition 2'. Clearly Condition 1 implies Condition 2, and both conditions suggest that A is some kind of weak ideal of B. This paper explores the extent to which this is true. The paper grew out of the author's attempts [1, 3] to generalize the Stone-Weierstrass theorem to C*-algebras.

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.

scholarly journals Noncommutative Lattices and the Algebras of Their Continuous Functions

1998 ◽  
Vol 10 (04) ◽  
pp. 439-466 ◽  
Author(s):  
Elisa Ercolessi ◽  
Giovanni Landi ◽  
Paulo Teotonio-Sobrinho
Keyword(s):  
Quantum Physics ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Hausdorff Topology ◽  
Topological Information ◽  
C Algebras ◽  
Finite Dimensional ◽  
Noncommutative Algebras ◽  
Af Algebras ◽  
The Continuum

Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset with a nontrivial non-Hausdorff topology. Their ability to reproduce important topological information of the continuum has been the main motivation for their use in quantum physics. Posets are truly noncommutative spaces, or noncommutative lattices, since they can be realized as structure spaces of noncommutative C*-algebras. These noncommutative algebras play the same rôle as the algebra of continuous functions [Formula: see text] on a Hausdorff topological space M and can be thought of as algebras of operator valued functions on posets. In this article, we will review some mathematical results that establish a duality between finite posets and a certain class of C*-algebras. We will see that the algebras in question are all postliminal approximately finite dimensional (AF) algebras.

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