INCLUSIONS OF C*-ALGEBRAS OF GRADED GROUPOIDS

被引：0

作者：

Armstrong, Becky ^{[1
]}

Clark, Lisa Orloff ^{[2
]}

An Huef, Astrid ^{[2
]}

机构：

[1] WWU Munster, Math Inst, Einsteinstr 62, D-48149 Munster, Germany

[2] Victoria Univ Wellington, Sch Math & Stat, POB 600, Wellington 6140, Aotearoa New Ze, New Zealand

来源：

JOURNAL OF OPERATOR THEORY | 2023年 / 89卷 / 01期

关键词：

Groupoid; C*-algebra; topological grading; isometric inclusion;

D O I：

10.7900/jot.2021aug26.2353

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a locally compact Hausdorff groupoid G which is graded over a discrete group. Then the fibre over the identity is an open and closed subgroupoid Ge. We show that both the full and reduced C*-algebras of this subgroupoid embed isometrically into the full and reduced C*-algebras of G; this extends a theorem of Kaliszewski-Quigg-Raeburn from the etale to the nonetale setting. As an application we show that the full and reduced C* -algebras of G are topologically graded in the sense of Exel, and we discuss the full and reduced C*-algebras of the associated bundles.

引用

页码：285 / 299

页数：15

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