连续代数的有理稳定性

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of the Australian Mathematical Society Pub Date : 2022-05-10 DOI:10.1017/s144678872200009x

Apurva Seth, P. Vaidyanathan

{"title":"连续代数的有理稳定性","authors":"Apurva Seth, P. Vaidyanathan","doi":"10.1017/s144678872200009x","DOIUrl":null,"url":null,"abstract":"\n We show that the properties of being rationally K-stable passes from the fibres of a continuous \n \n \n \n$C(X)$\n\n \n -algebra to the ambient algebra, under the assumption that the underlying space X is compact, metrizable, and of finite covering dimension. As an application, we show that a crossed product C*-algebra is (rationally) K-stable provided the underlying C*-algebra is (rationally) K-stable, and the action has finite Rokhlin dimension with commuting towers.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"39 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"RATIONAL -STABILITY OF CONTINUOUS -ALGEBRAS\",\"authors\":\"Apurva Seth, P. Vaidyanathan\",\"doi\":\"10.1017/s144678872200009x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n We show that the properties of being rationally K-stable passes from the fibres of a continuous \\n \\n \\n \\n$C(X)$\\n\\n \\n -algebra to the ambient algebra, under the assumption that the underlying space X is compact, metrizable, and of finite covering dimension. As an application, we show that a crossed product C*-algebra is (rationally) K-stable provided the underlying C*-algebra is (rationally) K-stable, and the action has finite Rokhlin dimension with commuting towers.\",\"PeriodicalId\":50007,\"journal\":{\"name\":\"Journal of the Australian Mathematical Society\",\"volume\":\"39 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Australian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s144678872200009x\",\"RegionNum\":4,\"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":"Journal of the Australian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s144678872200009x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了在假定底层空间X是紧的、可度量的、有限覆盖维数的前提下，理性k稳定的性质从连续的$C(X)$ -代数的纤维传递到周围代数。作为一个应用，我们证明了一个交叉积C*-代数是(合理)k稳定的，前提是底层C*-代数是(合理)k稳定的，并且具有交换塔的作用具有有限的Rokhlin维数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

RATIONAL -STABILITY OF CONTINUOUS -ALGEBRAS

We show that the properties of being rationally K-stable passes from the fibres of a continuous $C(X)$ -algebra to the ambient algebra, under the assumption that the underlying space X is compact, metrizable, and of finite covering dimension. As an application, we show that a crossed product C*-algebra is (rationally) K-stable provided the underlying C*-algebra is (rationally) K-stable, and the action has finite Rokhlin dimension with commuting towers.

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

Journal of the Australian Mathematical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Journal of the Australian Mathematical Society is the oldest journal of the Society, and is well established in its coverage of all areas of pure mathematics and mathematical statistics. It seeks to publish original high-quality articles of moderate length that will attract wide interest. Papers are carefully reviewed, and those with good introductions explaining the meaning and value of the results are preferred. Published Bi-monthly Published for the Australian Mathematical Society