{"title":"具有有限多理想的AH代数的分类","authors":"Kun Wang","doi":"10.7900/jot.2020dec04.2331","DOIUrl":null,"url":null,"abstract":"The class of AH algebras with the ideal property and no dimension growth is classified by the invariant inv(⋅). In this paper, we introduce a new invariant, Inv(⋅), a refined version of inv(⋅) and show that they are equivalent for AH algebras with the ideal property and no dimension growth. Then we give a sufficient condition under which the Hausdorffified algebraic K1 group could be recovered from the traditional Elliott invariant. As an application, the class of AH algebras with the ideal property, no dimension growth, and finitely many ideals can be classified by the extended Elliott invariant.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Classification of AH algebras with finitely many ideals\",\"authors\":\"Kun Wang\",\"doi\":\"10.7900/jot.2020dec04.2331\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The class of AH algebras with the ideal property and no dimension growth is classified by the invariant inv(⋅). In this paper, we introduce a new invariant, Inv(⋅), a refined version of inv(⋅) and show that they are equivalent for AH algebras with the ideal property and no dimension growth. Then we give a sufficient condition under which the Hausdorffified algebraic K1 group could be recovered from the traditional Elliott invariant. As an application, the class of AH algebras with the ideal property, no dimension growth, and finitely many ideals can be classified by the extended Elliott invariant.\",\"PeriodicalId\":50104,\"journal\":{\"name\":\"Journal of Operator Theory\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Operator Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7900/jot.2020dec04.2331\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7900/jot.2020dec04.2331","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Classification of AH algebras with finitely many ideals
The class of AH algebras with the ideal property and no dimension growth is classified by the invariant inv(⋅). In this paper, we introduce a new invariant, Inv(⋅), a refined version of inv(⋅) and show that they are equivalent for AH algebras with the ideal property and no dimension growth. Then we give a sufficient condition under which the Hausdorffified algebraic K1 group could be recovered from the traditional Elliott invariant. As an application, the class of AH algebras with the ideal property, no dimension growth, and finitely many ideals can be classified by the extended Elliott invariant.
期刊介绍:
The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.