The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations

被引：4

作者：

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

Vdovina, Alina ^{[3
]}

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

[3] Univ Newcastle, Sch Math Stat & Phys, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

来源：

JOURNAL OF NONCOMMUTATIVE GEOMETRY | 2021年 / 15卷 / 01期

关键词：

Inverse semigroups; Stone duality; ample groupoids; Cuntz-Krieger relations; REPRESENTATIONS; ALGEBRAS; GROUPOIDS; MONOIDS;

D O I：

10.4171/JNCG/400

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is a contribution to the theory of what might be termed 0-dimensional non-commutative spaces. We prove that associated with each inverse semigroup S is a Boolean inverse semigroup presented by the abstract versions of the Cuntz-Krieger relations. We call this Boolean inverse semigroup the tight completion of S and show that it arises from Exel's tight groupoid under non-commutative Stone duality.

引用

页码：279 / 304

页数：26