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
收藏
页码：285 / 299
页数：15
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