Classification of AF-Algebras

2010 ◽  
pp. 109-132
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
Af 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 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.

scholarly journals The Category of Bratteli Diagrams

2015 ◽  
Vol 67 (5) ◽  
pp. 990-1023 ◽  
Author(s):  
Massoud Amini ◽  
George A. Elliott ◽  
Nasser Golestani
Keyword(s):  
Point Of View ◽  
Category Structure ◽  
Bratteli Diagrams ◽  
K Theory ◽  
Af Algebras ◽  
Categorical Point

AbstractA category structure for Bratteli diagrams is proposed and a functor from the category of AF algebras to the category of Bratteli diagrams is constructed. Since isomorphism of Bratteli diagrams in this category coincides with Bratteli’s notion of equivalence, we obtain in particular a functorial formulation of Bratteli’s classification of AF algebras (and at the same time, of Glimm’s classification of UHF algebras). It is shown that the three approaches to classification of AF algebras, namely, through Bratteli diagrams, K-theory, and a certain natural abstract classifying category, are essentially the same from a categorical point of view.

Classification of spatial Lp AF algebras

2020 ◽  
Vol 31 (13) ◽  
pp. 2050088
Author(s):  
N. Christopher Phillips ◽  
Maria Grazia Viola
Keyword(s):  
Operator Algebra ◽  
Operator Algebras ◽  
Banach Algebras ◽  
Classification Theorem ◽  
Af Algebras

We define spatial [Formula: see text] AF algebras for [Formula: see text], and prove the following analog of the Elliott AF algebra classification theorem. If [Formula: see text] and [Formula: see text] are spatial [Formula: see text] AF algebras, then the following are equivalent: [Formula: see text] and [Formula: see text] have isomorphic scaled preordered [Formula: see text]-groups. [Formula: see text] as rings. [Formula: see text] (not necessarily isometrically) as Banach algebras. [Formula: see text] is isometrically isomorphic to [Formula: see text] as Banach algebras. [Formula: see text] is completely isometrically isomorphic to [Formula: see text] as matricial [Formula: see text] operator algebras. As background, we develop the theory of matricial [Formula: see text] operator algebras, and show that there is a unique way to make a spatial [Formula: see text] AF algebra into a matricial [Formula: see text] operator algebra. We also show that any countable scaled Riesz group can be realized as the scaled preordered [Formula: see text]-group of a spatial [Formula: see text] AF algebra.

scholarly journals Classification of certain inductive limit actions of compact groups on af algebras

2020 ◽  
pp. 2050128
Author(s):  
Qingyun Wang
Keyword(s):  
Compact Group ◽  
Inductive Limit ◽  
Complete Classification ◽  
Compact Groups ◽  
C Algebra ◽  
Finite Dimensional ◽  
K Theory ◽  
Af Algebras

Let [Formula: see text] be an AF algebra, [Formula: see text] be a compact group. We consider inductive limit actions of the form [Formula: see text], where [Formula: see text] is an action on the finite-dimensional C*-algebra [Formula: see text] which fixes each matrix summand. We give a complete classification up to conjugacy of such actions using twisted equivariant K-theory.

One-Parameter Continuous Fields of Kirchberg Algebras. II

2011 ◽  
Vol 63 (3) ◽  
pp. 500-532 ◽  
Author(s):  
Marius Dadarlat ◽  
George A. Elliott ◽  
Zhuang Niu
Keyword(s):  
One Dimension ◽  
Continuous Fields ◽  
Dimension One ◽  
Af Algebras ◽  
Torsion Free

Abstract Parallel to the first two authors’ earlier classification of separable, unital, one-parameter, continuous fields of Kirchberg algebras with torsion free K-groups supported in one dimension, one-parameter, separable, unital, continuous fields of AF-algebras are classified by their ordered K0-sheaves. Effros-Handelman-Shen type theorems are proved for separable unital one-parameter continuous fields of AF-algebras and Kirchberg algebras.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

1970 ◽  
Vol 28 ◽  
pp. 220-221
Author(s):  
Gerald Fine ◽  
Azorides R. Morales
Keyword(s):  
Cardiac Myxoma ◽  
Osteogenic Sarcoma ◽  
Diagnostic Value ◽  
Soft Tissue Tumors ◽  
Amelanotic Melanoma ◽  
Growth Patterns ◽  
Light Microscopic Level ◽  
Mesenchymal Tumors ◽  
Good Agreement

For years the separation of carcinoma and sarcoma and the subclassification of sarcomas has been based on the appearance of the tumor cells and their microscopic growth pattern and information derived from certain histochemical and special stains. Although this method of study has produced good agreement among pathologists in the separation of carcinoma from sarcoma, it has given less uniform results in the subclassification of sarcomas. There remain examples of neoplasms of different histogenesis, the classification of which is questionable because of similar cytologic and growth patterns at the light microscopic level; i.e. amelanotic melanoma versus carcinoma and occasionally sarcoma, sarcomas with an epithelial pattern of growth simulating carcinoma, histologically similar mesenchymal tumors of different histogenesis (histiocytoma versus rhabdomyosarcoma, lytic osteogenic sarcoma versus rhabdomyosarcoma), and myxomatous mesenchymal tumors of diverse histogenesis (myxoid rhabdo and liposarcomas, cardiac myxoma, myxoid neurofibroma, etc.)

Ultrastructure of mesotheliomas

1984 ◽  
Vol 42 ◽  
pp. 98-101
Author(s):  
Irving Dardick
Keyword(s):  
Electron Microscopy ◽  
Latent Period ◽  
Spindle Cell ◽  
Spindle Cell Sarcoma ◽  
Metastatic Adenocarcinoma ◽  
Cell Sarcoma ◽  
Cytological Features ◽  
Industrial Use ◽  
Degree Of Differentiation

With the extensive industrial use of asbestos in this century and the long latent period (20-50 years) between exposure and tumor presentation, the incidence of malignant mesothelioma is now increasing. Thus, surgical pathologists are more frequently faced with the dilemma of differentiating mesothelioma from metastatic adenocarcinoma and spindle-cell sarcoma involving serosal surfaces. Electron microscopy is amodality useful in clarifying this problem.In utilizing ultrastructural features in the diagnosis of mesothelioma, it is essential to appreciate that the classification of this tumor reflects a variety of morphologic forms of differing biologic behavior (Table 1). Furthermore, with the variable histology and degree of differentiation in mesotheliomas it might be expected that the ultrastructure of such tumors also reflects a range of cytological features. Such is the case.

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