scholarly journals Stable rank and real rank of compact transformation group C*-algebras

2006 ◽  
Vol 175 (2) ◽  
pp. 103-120 ◽  
Author(s):  
Robert J. Archbold ◽  
Eberhard Kaniuth
Keyword(s):  
Transformation Group ◽  
Stable Rank ◽  
Real Rank ◽  
C Algebras ◽  
Compact Transformation Group

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 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 $C^*(G)$.

Stable Rank of Some Full Group C*-Algebras of Groups Obtained by the Free Product

1997 ◽  
Vol 08 (03) ◽  
pp. 375-382 ◽  
Author(s):  
Masaru Nagisa
Keyword(s):  
Free Product ◽  
Free Group ◽  
Finite Groups ◽  
Stable Rank ◽  
Real Rank ◽  
Full Group ◽  
The Real ◽  
C Algebras

We compute the real rank and the stable rank of full group C*-algebras. Main result is (i) rr (C*(Fn)) = ∞, (ii) sr (C*(G1 * G2)) = ∞(|G1| ≥ 2, |G2| ≥ 2 and |G1| + |G2| ≥ 5), (iii) sr (C*(G1 * G2)) = 1(|G1| = |G2| = 2), where Fn is the free group with n generators, G1 and G2 are finite groups and |G| means the order of the group G.

scholarly journals C*-algebras of a Cantor system with finitely many minimal subsets: structures, K-theories, and the index map

2020 ◽  
pp. 1-46 ◽  
Author(s):  
SERGEY BEZUGLYI ◽  
ZHUANG NIU ◽  
WEI SUN
Keyword(s):  
Directed Graphs ◽  
Cantor Set ◽  
Stable Rank ◽  
Crossed Product ◽  
Real Rank ◽  
C Algebra ◽  
C Algebras ◽  
Rank 2 ◽  
Stably Finite ◽  
The Ideal

We study homeomorphisms of a Cantor set with $k$ ( $k<+\infty$ ) minimal invariant closed (but not open) subsets; we also study crossed product C*-algebras associated to these Cantor systems and certain of their orbit-cut sub-C*-algebras. In the case where $k\geq 2$ , the crossed product C*-algebra is stably finite, has stable rank 2, and has real rank 0 if in addition $(X,\unicode[STIX]{x1D70E})$ is aperiodic. The image of the index map is connected to certain directed graphs arising from the Bratteli–Vershik–Kakutani model of the Cantor system. Using this, it is shown that the ideal of the Bratteli diagram (of the Bratteli–Vershik–Kakutani model) must have at least $k$ vertices at each level, and the image of the index map must consist of infinitesimals.

scholarly journals On the topological stable rank of certain transformation group C*-algebras

1990 ◽  
Vol 10 (1) ◽  
pp. 197-207 ◽  
Author(s):  
Ian F. Putnam
Keyword(s):  
Transformation Group ◽  
Metrizable Space ◽  
Stable Rank ◽  
Residual Finiteness ◽  
Dynamical Condition ◽  
C Algebras ◽  
Compact Metrizable Space ◽  
Topological Stable Rank ◽  
Necessary And Sufficient ◽  
Totally Disconnected

AbstractWe consider the crossed product or transformation group C*-algebras arising from actions of the group of integers on a totally disconnected compact metrizable space. Under a mild hypothesis, we give a necessary and sufficient dynamical condition for the invertibles in such a C*-algebra to be dense. We also examine the property of residual finiteness for such C*-algebras.

scholarly journals Stable rank and real rank of graph C∗-algebras

2001 ◽  
Vol 200 (2) ◽  
pp. 331-343 ◽  
Author(s):  
J.A. Jeong ◽  
G.H. Park ◽  
D.Y. Shin
Keyword(s):  
Stable Rank ◽  
Real Rank ◽  
C Algebras

scholarly journals Stable rank and real rank for some classes of group $C^\ast $-algebras

2005 ◽  
Vol 357 (6) ◽  
pp. 2165-2186 ◽  
Author(s):  
Robert J. Archbold ◽  
Eberhard Kaniuth
Keyword(s):  
Stable Rank ◽  
Real Rank
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