Groupoid models for the C*-algebras of topological higher-rank graphs

被引：0

作者：

Yeend, Trent ^{[1
]}

机构：

[1] Univ Newcastle, Sch Math & Phys Sci, Newcastle, NSW 2308, Australia

来源：

JOURNAL OF OPERATOR THEORY | 2007年 / 57卷 / 01期

关键词：

topological graph; higher rank graph; groupoid; graph algebra; Cuntz-Krieger algebra;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide groupoid models for Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs. Extending groupoid models used in the theory of graph algebras and topological dynamical systems to our setting, we prove results on essential freeness and amenability of the groupoids which capture the existing theory, and extend results involving group crossed products of graph algebras.

引用

页码：95 / 120

页数：26

共 31 条

[1]

[Anonymous], MONOGRAPH ENSEIGN MA

[2]

Arzumanian V, 1996, OPERATOR ALGEBRAS AND QUANTUM FIELD THEORY, P93

[3]

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

[4] GROUPOIDS ASSOCIATED WITH ENDOMORPHISMS [J].

DEACONU, V .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (05) :1779-1786

[5] The C*-algebras of arbitrary graphs [J].

Drinen, D ;

Tomforde, M .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2005, 35 (01) :105-135

[6] Higher-rank graph C*-algebras:: An inverse semigroup and groupoid approach [J].

Farthing, C ;

Muhly, PS ;

Yeend, T .

SEMIGROUP FORUM, 2005, 71 (02) :159-187

[7]

Fowler NJ, 1999, INDIANA U MATH J, V48, P155

[8] The C*-algebras of infinite graphs [J].

Fowler, NJ ;

Laca, M ;

Raeburn, I .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (08) :2319-2327

[9]

Kaliszewski S, 2001, J OPERAT THEOR, V46, P411

[10] A class of C*-algebras generalizing both graph algebras and homeomorphism C*-algebras I, fundamental results [J].

Katsura, T .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (11) :4287-4322

← 1 2 3 4 →