{"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}
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.
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
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