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.

scholarly journals Homogeneity of the Pure State Space of a Separable C*-Algebra

2003 ◽  
Vol 46 (3) ◽  
pp. 365-372 ◽  
Author(s):  
Akitaka Kishimoto ◽  
Narutaka Ozawa ◽  
Shôichirô Sakai
Keyword(s):  
Automorphism Group ◽  
State Space ◽  
Pure State ◽  
C Algebra ◽  
Inner Automorphisms

AbstractWe prove that the pure state space is homogeneous under the action of the automorphism group (or the subgroup of asymptotically inner automorphisms) for all the separable simple C*-algebras. The first result of this kind was shown by Powers for the UHF algbras some 30 years ago.

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.

A FUNCTIONAL REPRESENTATION FOR NON-COMMUTATIVE C*-ALGEBRAS

1994 ◽  
Vol 06 (05) ◽  
pp. 675-697 ◽  
Author(s):  
RENZO CIRELLI ◽  
ALESSANDRO MANIÀ ◽  
LIVIO PIZZOCCHERO
Keyword(s):  
State Space ◽  
Pure State ◽  
C Algebras ◽  
Functional Representation ◽  
Function Algebras

We obtain a representation of non commutative C*-algebras as function algebras on the pure state space, with a convenient product. This construction is an extension of the classical functional representation of commutative C*-algebras.

scholarly journals On the automorphism group of certain simple $C^*$-algebras

2004 ◽  
Vol 95 (2) ◽  
pp. 245
Author(s):  
Jesper Mygind
Keyword(s):  
Automorphism Group ◽  
Group Of Automorphisms ◽  
C Algebras ◽  
Inner Automorphisms

We show that the information contained in $KL(A,B)$ is determined by other invariants when $A$ and $B$ are certain simple unital projectionless $C^*$-algebras. This allows us to compute the group of automorphisms modulo the group of approximately inner automorphisms in terms of the Elliott invariant.

On Automorphisms and Derivations of a Lie Algebra

2006 ◽  
Vol 13 (01) ◽  
pp. 119-132 ◽  
Author(s):  
V. R. Varea ◽  
J. J. Varea
Keyword(s):  
Automorphism Group ◽  
Normal Subgroup ◽  
Large Class ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Finite Dimension ◽  
Nilpotent Lie Algebra ◽  
Identity Component ◽  
Trivial Center

We study automorphisms and derivations of a Lie algebra L of finite dimension satisfying certain centrality conditions. As a consequence, we obtain that every nilpotent normal subgroup of the automorphism group of L is unipotent for a very large class of Lie algebras. This result extends one of Leger and Luks. We show that the automorphism group of a nilpotent Lie algebra can have trivial center and have yet a unipotent identity component.

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 Graphs With Stability Index One

1976 ◽  
Vol 22 (2) ◽  
pp. 212-220 ◽  
Author(s):  
D. A. Holton ◽  
J. A. Sims
Keyword(s):  
Automorphism Group ◽  
Large Class ◽  
Cartesian Product ◽  
Sufficient Conditions ◽  
Stability Index ◽  
Arbitrary Graph ◽  
Stability Properties ◽  
The Stability

AbstractWe consider the effect on the stability properties of a graph G, of the presence in the automorphism group of G of automorphisms (uv)h, where u and v are vertices of G, and h is a permutation of vertices of G excluding u and v. We find sufficient conditions for an arbitrary graph and a cartesian product to have stability index one, and conjecture in the latter case that they are necessary. Finally we exhibit explicitly a large class of graphs which have stability index one.

scholarly journals Homogeneity of the Pure State Space of the Cuntz Algebra

2000 ◽  
Vol 171 (2) ◽  
pp. 331-345 ◽  
Author(s):  
Ola Bratteli ◽  
Akitaka Kishimoto
Keyword(s):  
State Space ◽  
Pure State ◽  
Cuntz Algebra

Bratteli diagrams via the De Concini–Procesi theorem

2020 ◽  
pp. 2050073
Author(s):  
Daniele Mundici
Keyword(s):  
Large Class ◽  
Word Problem ◽  
Bratteli Diagram ◽  
Von Neumann ◽  
Generators And Relations ◽  
The Core ◽  
Bratteli Diagrams ◽  
Group Presentations ◽  
Almost All ◽  
Af Algebras

An AF algebra [Formula: see text] is said to be an AF[Formula: see text] algebra if the Murray–von Neumann order of its projections is a lattice. Many, if not most, of the interesting classes of AF algebras existing in the literature are AF[Formula: see text] algebras. We construct an algorithm which, on input a finite presentation (by generators and relations) of the Elliott semigroup of an AF[Formula: see text] algebra [Formula: see text], generates a Bratteli diagram of [Formula: see text] We generalize this result to the case when [Formula: see text] has an infinite presentation with a decidable word problem, in the sense of the classical theory of recursive group presentations. Applications are given to a large class of AF algebras, including almost all AF algebras whose Bratteli diagram is explicitly described in the literature. The core of our main algorithms is a combinatorial-polyhedral version of the De Concini–Procesi theorem on the elimination of points of indeterminacy in toric varieties.

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