关于与最小位移空间相关的cuntz-pimsner c *-代数的核维

IF 0.6 3区数学 Q3 MATHEMATICS Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2021-12-31 DOI:10.4153/S0008414X22000645

Zhuofeng He, Sihan Wei

{"title":"关于与最小位移空间相关的cuntz-pimsner c *-代数的核维","authors":"Zhuofeng He, Sihan Wei","doi":"10.4153/S0008414X22000645","DOIUrl":null,"url":null,"abstract":"For every one-sided shift space $X$ over a finite alphabet, left special elements are those points in $X$ having at least two preimages under the shift operation. In this paper, we show that the Cuntz-Pimsner $C^*$-algebra $\\mathcal{O}_X$ has nuclear dimension 1 when $X$ is minimal and the number of left special elements in $X$ is finite. This is done by describing thoroughly the cover of $X$ which also recovers an exact sequence, discovered before by T. Carlsen and S. Eilers.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A NOTE ON THE NUCLEAR DIMENSION OF CUNTZ-PIMSNER C*-ALGEBRAS ASSOCIATED WITH MINIMAL SHIFT SPACES\",\"authors\":\"Zhuofeng He, Sihan Wei\",\"doi\":\"10.4153/S0008414X22000645\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For every one-sided shift space $X$ over a finite alphabet, left special elements are those points in $X$ having at least two preimages under the shift operation. In this paper, we show that the Cuntz-Pimsner $C^*$-algebra $\\\\mathcal{O}_X$ has nuclear dimension 1 when $X$ is minimal and the number of left special elements in $X$ is finite. This is done by describing thoroughly the cover of $X$ which also recovers an exact sequence, discovered before by T. Carlsen and S. Eilers.\",\"PeriodicalId\":55284,\"journal\":{\"name\":\"Canadian Journal of Mathematics-Journal Canadien De Mathematiques\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Canadian Journal of Mathematics-Journal Canadien De Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4153/S0008414X22000645\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4153/S0008414X22000645","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

对于有限字母表上的每一个单侧移位空间$X$，左特殊元素是在$X$中至少有两个在移位操作下的原像的点。本文证明了当$X$为最小值且$X$的左特殊元素个数有限时，Cuntz-Pimsner $C^*$-代数$\mathcal{O}_X$具有核维数1。这是通过彻底描述$X$的封面来完成的，它也恢复了T. Carlsen和S. Eilers之前发现的精确序列。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

A NOTE ON THE NUCLEAR DIMENSION OF CUNTZ-PIMSNER C*-ALGEBRAS ASSOCIATED WITH MINIMAL SHIFT SPACES

For every one-sided shift space $X$ over a finite alphabet, left special elements are those points in $X$ having at least two preimages under the shift operation. In this paper, we show that the Cuntz-Pimsner $C^*$-algebra $\mathcal{O}_X$ has nuclear dimension 1 when $X$ is minimal and the number of left special elements in $X$ is finite. This is done by describing thoroughly the cover of $X$ which also recovers an exact sequence, discovered before by T. Carlsen and S. Eilers.

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

来源期刊

Canadian Journal of Mathematics-Journal Canadien De Mathematiques 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4.5 months

期刊介绍： The Canadian Journal of Mathematics (CJM) publishes original, high-quality research papers in all branches of mathematics. The Journal is a flagship publication of the Canadian Mathematical Society and has been published continuously since 1949. New research papers are published continuously online and collated into print issues six times each year. To be submitted to the Journal, papers should be at least 18 pages long and may be written in English or in French. Shorter papers should be submitted to the Canadian Mathematical Bulletin. Le Journal canadien de mathématiques (JCM) publie des articles de recherche innovants de grande qualité dans toutes les branches des mathématiques. Publication phare de la Société mathématique du Canada, il est publié en continu depuis 1949. En ligne, la revue propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés six fois par année. Les textes présentés au JCM doivent compter au moins 18 pages et être rédigés en anglais ou en français. C’est le Bulletin canadien de mathématiques qui reçoit les articles plus courts.