scholarly journals Classification of Graph C ∗-Algebras with No More than Four Primitive Ideals

2013 ◽  
pp. 89-129 ◽  
Author(s):  
Søren Eilers ◽  
Gunnar Restorff ◽  
Efren Ruiz
Keyword(s):  
C Algebras ◽  
Primitive Ideals

scholarly journals Classification of real rank zero, purely infinite C⁎-algebras with at most four primitive ideals

2016 ◽  
Vol 271 (7) ◽  
pp. 1921-1947
Author(s):  
Sara E. Arklint ◽  
Gunnar Restorff ◽  
Efren Ruiz
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras ◽  
Primitive Ideals

On classification of non-unital amenable simple C*-algebras, II

2020 ◽  
Vol 158 ◽  
pp. 103865
Author(s):  
Guihua Gong ◽  
Huaxin Lin
Keyword(s):  
C Algebras

scholarly journals Primitive ideals, twisting functors and star actions for classical Lie superalgebras

2016 ◽  
Vol 2016 (718) ◽  
Author(s):  
Kevin Coulembier ◽  
Volodymyr Mazorchuk
Keyword(s):  
Representation Theory ◽  
Lie Superalgebras ◽  
Simple Modules ◽  
Primitive Ideals

AbstractWe study three related topics in representation theory of classical Lie superalgebras. The first one is classification of primitive ideals, i.e. annihilator ideals of simple modules, and inclusions between them. The second topic concerns Arkhipov’s twisting functors on the BGG category

scholarly journals The Primitive Ideals of some Étale Groupoid C ∗-Algebras

2015 ◽  
Vol 19 (2) ◽  
pp. 255-276 ◽  
Author(s):  
Aidan Sims ◽  
Dana P. Williams
Keyword(s):  
C Algebras ◽  
Primitive Ideals ◽  
Étale Groupoid

scholarly journals ON THE CLASSIFICATION OF NUCLEAR C*-ALGEBRAS

2002 ◽  
Vol 85 (1) ◽  
pp. 168-210 ◽  
Author(s):  
MARIUS DADARLAT ◽  
SØREN EILERS
Keyword(s):  
Subject Classification ◽  
Unified Approach ◽  
C Algebras ◽  
Starting Point ◽  
K Theory

We employ results from KK-theory, along with quasidiagonality techniques, to obtain wide-ranging classification results for nuclear C*-algebras. Using a new realization of the Cuntz picture of the Kasparov groups we show that two morphisms inducing equal KK-elements are approximately stably unitarily equivalent. Using K-theory with coefficients to associate a partial KK-element to an approximate morphism, our result is generalized to cover such maps. Conversely, we study the problem of lifting a (positive) partial KK-element to an approximate morphism. These results are employed to obtain classification results for certain classes of quasidiagonal C*-algebras introduced by H. Lin, and to reprove the classification of purely infinite simple nuclear C*-algebras of Kirchberg and Phillips. It is our hope that this work can be the starting point of a unified approach to the classification of nuclear C*-algebras.2000 Mathematical Subject Classification: primary 46L35; secondary 19K14, 19K35, 46L80.

scholarly journals On the classification of C*-algebras of real rank zero, III: The infinite case

1998 ◽  
pp. 11-72 ◽  
Author(s):  
Ola Bratteli ◽  
George Elliott ◽  
David Evans ◽  
Akitaka Kishimoto
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras ◽  
Infinite Case

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 Inductive limit of direct sums of simple TAI algebras

2019 ◽  
pp. 1-26
Author(s):  
Bo Cui ◽  
Chunlan Jiang ◽  
Liangqing Li
Keyword(s):  
Inductive Limit ◽  
Direct Sums ◽  
Rank Zero ◽  
C Algebra ◽  
C Algebras ◽  
Rank One ◽  
Tracial Rank ◽  
Ideal Property ◽  
Funct Anal

An ATAI (or ATAF, respectively) algebra, introduced in [C. Jiang, A classification of non simple C*-algebras of tracial rank one: Inductive limit of finite direct sums of simple TAI C*-algebras, J. Topol. Anal. 3 (2011) 385–404] (or in [X. C. Fang, The classification of certain non-simple C*-algebras of tracial rank zero, J. Funct. Anal. 256 (2009) 3861–3891], respectively) is an inductive limit [Formula: see text], where each [Formula: see text] is a simple separable nuclear TAI (or TAF) C*-algebra with UCT property. In [C. Jiang, A classification of non simple C*-algebras of tracial rank one: Inductive limit of finite direct sums of simple TAI C*-algebras, J. Topol. Anal. 3 (2011) 385–404], the second author classified all ATAI algebras by an invariant consisting orderd total [Formula: see text]-theory and tracial state spaces of cut down algebras under an extra restriction that all element in [Formula: see text] are torsion. In this paper, we remove this restriction, and obtained the classification for all ATAI algebras with the Hausdorffized algebraic [Formula: see text]-group as an addition to the invariant used in [C. Jiang, A classification of non simple C*-algebras of tracial rank one: Inductive limit of finite direct sums of simple TAI C*-algebras, J. Topol. Anal. 3 (2011) 385–404]. The theorem is proved by reducing the class to the classification theorem of [Formula: see text] algebras with ideal property which is done in [G. Gong, C. Jiang and L. Li, A classification of inductive limit C*-algebras with ideal property, preprint (2016), arXiv:1607.07681]. Our theorem generalizes the main theorem of [X. C. Fang, The classification of certain non-simple C*-algebras of tracial rank zero, J. Funct. Anal. 256 (2009) 3861–3891], [C. Jiang, A classification of non simple C*-algebras of tracial rank one: Inductive limit of finite direct sums of simple TAI C*-algebras, J. Topol. Anal. 3 (2011) 385–404] (see Corollary 4.3).

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