关于逆半群的$C^*$-代数的核性

Pub Date : 2020-07-01 DOI:10.5565/publmat6422005

M. Amini, M. Khoshkam

{"title":"关于逆半群的$C^*$-代数的核性","authors":"M. Amini, M. Khoshkam","doi":"10.5565/publmat6422005","DOIUrl":null,"url":null,"abstract":": We show that the universal groupoid of an inverse semigroup S is topo- logically (measurewise) amenable if and only if S is hyperﬁnite and all members of a family of subsemigroups of S indexed by the spectrum of the commutative C ∗ -al-gebra C ∗ ( E S ) on the idempotents E S of S are amenable. Thereby we solve some problems raised by A. L. T. Paterson.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On nuclearity of the $C^*$-algebra of an inverse semigroup\",\"authors\":\"M. Amini, M. Khoshkam\",\"doi\":\"10.5565/publmat6422005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": We show that the universal groupoid of an inverse semigroup S is topo- logically (measurewise) amenable if and only if S is hyperﬁnite and all members of a family of subsemigroups of S indexed by the spectrum of the commutative C ∗ -al-gebra C ∗ ( E S ) on the idempotents E S of S are amenable. Thereby we solve some problems raised by A. L. T. Paterson.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5565/publmat6422005\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5565/publmat6422005","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

：我们证明了逆半群S的泛群胚在拓扑上（度量上）是可服从的，当且仅当S是超有限的，并且由S的幂等元ES上的交换C*-al gebra C*（ES）的谱索引的S的子半群族的所有成员都可服从。从而解决了帕特森提出的一些问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

On nuclearity of the $C^*$-algebra of an inverse semigroup

: We show that the universal groupoid of an inverse semigroup S is topo- logically (measurewise) amenable if and only if S is hyperﬁnite and all members of a family of subsemigroups of S indexed by the spectrum of the commutative C ∗ -al-gebra C ∗ ( E S ) on the idempotents E S of S are amenable. Thereby we solve some problems raised by A. L. T. Paterson.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助