scholarly journals On the stable rank of simple C*-algebras

1999 ◽  
Vol 12 (4) ◽  
pp. 1091-1102 ◽  
Author(s):  
Jesper Villadsen
Keyword(s):  
Stable Rank ◽  
C Algebras

scholarly journals STABLE RANK FOR INCLUSIONS OF C*-ALGEBRAS

2008 ◽  
Vol 19 (09) ◽  
pp. 1011-1020 ◽  
Author(s):  
HIROYUKI OSAKA
Keyword(s):  
Finite Groups ◽  
Stable Rank ◽  
C Algebra ◽  
C Algebras ◽  
Rank One ◽  
Common Unit ◽  
Topological Stable Rank

When a unital C*-algebra A has topological stable rank one (write tsr (A) = 1), we know that tsr (pAp) = 1 for a non-zero projection p ∈ A. When, however, tsr (A) ≥ 2, it is generally false. We prove that if a unital C*-algebra A has a simple unital C*-subalgebra D of A with common unit such that D has Property (SP) and sup p ∈ P(D) tsr (pAp) < ∞, then tsr (A) ≤ 2. As an application let A be a simple unital C*-algebra with tsr (A) = 1 and Property (SP), [Formula: see text] finite groups, αk actions from Gk to Aut ((⋯((A × α1 G1) ×α2 G2)⋯) ×αk-1 Gk-1). (G0 = {1}). Then [Formula: see text]

scholarly journals SOFT C*-ALGEBRAS

2002 ◽  
Vol 45 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Carla Farsi
Keyword(s):  
Stable Rank ◽  
Crossed Product ◽  
Subject Classification ◽  
Large Classes ◽  
C Algebras ◽  
Primary 46L80

AbstractIn this paper we consider soft group and crossed product $C^*$-algebras. In particular we show that soft crossed product $C^*$-algebras are isomorphic to classical crossed product $C^*$-algebras. We also prove that large classes of soft $C^*$-algebras have stable rank equal to infinity.AMS 2000 Mathematics subject classification: Primary 46L80; 46L55

scholarly journals Ideal structure and $C^*$-algebras of low rank

2007 ◽  
Vol 100 (1) ◽  
pp. 5 ◽  
Author(s):  
Lawrence G. Brown ◽  
Gert K. Pedersen
Keyword(s):  
Stable Rank ◽  
Low Rank ◽  
Real Rank ◽  
Ideal Structure ◽  
C Algebra ◽  
C Algebras ◽  
Rank One ◽  
The Relationship

We explore various constructions with ideals in a $C^*$-algebra $A$ in relation to the notions of real rank, stable rank and extremal richness. In particular we investigate the maximum ideals of low rank. And we investigate the relationship between existence of infinite or properly infinite projections in an extremally rich $C^*$-algebra and non-existence of ideals or quotients of stable rank one.

scholarly journals A revised augmented Cuntz semigroup

2021 ◽  
Vol 127 (1) ◽  
pp. 131-160
Author(s):  
Leonel Robert ◽  
Luis Santiago
Keyword(s):  
Stable Rank ◽  
Inductive Limits ◽  
C Algebras ◽  
Exact Functor ◽  
Cw Complexes ◽  
Rank One ◽  
Cuntz Semigroup ◽  
Original Construction

We revise the construction of the augmented Cuntz semigroup functor used by the first author to classify inductive limits of $1$-dimensional noncommutative CW complexes. The original construction has good functorial properties when restricted to the class of C*-algebras of stable rank one. The construction proposed here has good properties for all C*-algebras: we show that the augmented Cuntz semigroup is a stable, continuous, split exact functor, from the category of C*-algebras to the category of Cu-semigroups.

scholarly journals Structure theory and stable rank for C*-algebras of finite higher-rank graphs

2021 ◽  
pp. 1-26
Author(s):  
David Pask ◽  
Adam Sierakowski ◽  
Aidan Sims
Keyword(s):  
Stable Rank ◽  
Structure Theory ◽  
C Algebras ◽  
Higher Rank ◽  
Stably Finite ◽  
Locally Convex

Abstract We study the structure and compute the stable rank of $C^{*}$ -algebras of finite higher-rank graphs. We completely determine the stable rank of the $C^{*}$ -algebra when the $k$ -graph either contains no cycle with an entrance or is cofinal. We also determine exactly which finite, locally convex $k$ -graphs yield unital stably finite $C^{*}$ -algebras. We give several examples to illustrate our results.

scholarly journals On the stable rank and real rank of group $C^*$-algebras of nilpotent locally compact groups

2005 ◽  
Vol 97 (1) ◽  
pp. 89
Author(s):  
Robert J. Archbold ◽  
Eberhard Kaniuth
Keyword(s):  
Abelian Group ◽  
Compact Group ◽  
Locally Compact Group ◽  
Stable Rank ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Real Rank ◽  
Locally Compact ◽  
C Algebras ◽  
Necessary And Sufficient

It is shown that if $G$ is an almost connected nilpotent group then the stable rank of $C^*(G)$ is equal to the rank of the abelian group $G/[G,G]$. For a general nilpotent locally compact group $G$, it is shown that finiteness of the rank of $G/[G,G]$ is necessary and sufficient for the finiteness of the stable rank of $C^*(G)$ and also for the finiteness of the real rank of $C^*(G)$.

Sign in / Sign up

Export Citation Format

Share Document