Higher-rank graphs and their C*-algebras

被引：96

作者：

Raeburn, I ^{[1
]}

Sims, A ^{[1
]}

Yeend, T ^{[1
]}

机构：

[1] Univ Newcastle, Dept Math, Callaghan, NSW 2308, Australia

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2003年 / 46卷

关键词：

graph algebra; Cuntz-Krieger algebra; uniqueness;

D O I：

10.1017/S0013091501000645

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz-Krieger algebras. We describe a variant of the Cuntz-Krieger relations which applies to graphs with sources, and describe a local convexity condition which characterizes the higher-rank graphs that admit a non-trivial Cuntz-Krieger family. We then prove versions of the uniqueness theorems and classifications of ideals for the C*-algebras generated by Cuntz-Krieger families.

引用

页码：99 / 115

页数：17

共 13 条

[1]

ADJI S, 1994, P AM MATH SOC, V122, P1133

[2]

Bates T., 2000, NEW YORK J MATH, V6, P307

[3] SHAPE-THEORY FOR C-STAR-ALGEBRAS [J].