Graph inverse semigroups: Their characterization and completion

被引：26

作者：

Jones, David G. ^{[1
]}

Lawson, Mark V. ^{[1
,2
]}

机构：

[1] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

[2] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland

来源：

JOURNAL OF ALGEBRA | 2014年 / 409卷

基金：

英国工程与自然科学研究理事会;

关键词：

Inverse semigroups; Free categories; Cuntz-Krieger algebras; POLYCYCLIC MONOIDS; CSTAR-ALGEBRAS; REPRESENTATIONS; GROUPOIDS;

D O I：

10.1016/j.jalgebra.2014.04.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of C*-algebras. In this paper, we characterize such semigroups and show how they may be completed, under suitable conditions, to form what we call the Cuntz-Krieger semigroup of the graph. This semigroup is proved to be the ample semigroup of a topological groupoid associated with the graph, and the semigroup analogue of the Leavitt path algebra of the graph. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：444 / 473

页数：30

共 39 条

[1] The Leavitt path algebra of a graph [J].

Abrams, G ;

Pino, GA .

JOURNAL OF ALGEBRA, 2005, 293 (02) :319-334

[2]

Ash C.J., 1975, Semigroup Forum, V11, P140, DOI DOI 10.1007/BF02195262

[3] ITERATION OF EXPANSIONS - UNAMBIGUOUS SEMIGROUPS [J].

BIRGET, JC .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1984, 34 (01) :1-55

[4]

Bratteli O., 1999, MEM AM MATH SOC, V663

[5] A CLASS OF D-SIMPLE SEMIGROUPS [J].

CLIFFORD, AH .

AMERICAN JOURNAL OF MATHEMATICS, 1953, 75 (04) :547-556

[6] SIMPLE CSTAR-ALGEBRAS GENERATED BY ISOMETRIES [J].

CUNTZ, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1977, 57 (02) :173-185

[7] CLASS OF CSTAR-ALGEBRAS AND TOPOLOGICAL MARKOV-CHAINS [J].

CUNTZ, J ;

KRIEGER, W .

INVENTIONES MATHEMATICAE, 1980, 56 (03) :251-268

[8] Semigroupoid C*-algebras [J].

Exel, R. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 377 (01) :303-318

[9] Tight representations of semilattices and inverse semigroups [J].

Exel, R. .

SEMIGROUP FORUM, 2009, 79 (01) :159-182

[10]

Howie J.M., 1995, Fundamentals of Semigroup Theory

← 1 2 3 4 →