A class of simple C*-algebras with stable rank one

被引：15

作者：

Elliott, George A.

Ho, Toan M. ^{[1
,2
]}

Toms, Andrew S. ^{[1
,2
]}

机构：

[1] York Univ, Dept Math & Stat, Toronto, ON M3J 193, Canada

[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2009年 / 256卷 / 02期

关键词：

All algebras; Stable rank; Dimension growth; REAL RANK; STAR-ALGEBRAS; ZERO; CLASSIFICATION; REDUCTION;

D O I：

10.1016/j.jfa.2008.08.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the limits of inductive sequences (A(i), phi(i)) where each A(i) is a direct sum of full matrix algebras over compact metric spaces and each partial map of phi(i) is diagonal. We give a new characterisation of simplicity for such algebras, and apply it to prove that the said algebras have stable rank one whenever they are simple and unital. Significantly, our results do not require any dimension growth assumption. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：307 / 322

页数：16

共 18 条

[1] THE REAL RANK OF INDUCTIVE LIMIT C-ASTERISK-ALGEBRAS
BLACKADAR, B
DADARLAT, M
RORDAM, M
[J]. MATHEMATICA SCANDINAVICA, 1991, 69 (02) : 211 - 216
[2] Blackadar B., 1993, RES NOTES MATH, V5, P11
[3] DADARLAT M, 1995, J REINE ANGEW MATH, V460, P189
[4] REDUCTION OF TOPOLOGICAL STABLE RANK IN INDUCTIVE LIMITS OF C-STAR-ALGEBRAS
DADARLAT, M
NAGY, G
NEMETHI, A
PASNICU, C
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1992, 153 (02) : 267 - 276
[5] THE STRUCTURE OF THE IRRATIONAL ROTATION C(ASTERISK)-ALGEBRA
ELLIOTT, GA
EVANS, DE
[J]. ANNALS OF MATHEMATICS, 1993, 138 (03) : 477 - 501
[6] ON THE CLASSIFICATION OF C-ASTERISK-ALGEBRAS OF REAL RANK ZERO
ELLIOTT, GA
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1993, 443 : 179 - 219
[7] On the classification of C*-algebras of real rank zero .2.
Elliott, GA
Gong, GH
[J]. ANNALS OF MATHEMATICS, 1996, 144 (03) : 497 - 610
[8] ELLIOTT GA, INVENT MATH IN PRESS
[9] Gong GH., 2002, DOC MATH, V7, P255
[10] RIESZ-DECOMPOSITION IN INDUCTIVE LIMIT C-ASTERISK-ALGEBRAS
GOODEARL, KR
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1994, 24 (04) : 1405 - 1430

← 1 2 →