具有有限多理想的AH代数的分类

IF 0.7 4区 数学 Q2 MATHEMATICS
Kun Wang
{"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}
引用次数: 2

摘要

用不变量inv(⋅)对一类具有理想性质且无维数增长的AH代数进行分类。本文引入了一个新的不变量Inv(⋅),即Inv(⋅)的改进版本,并证明了它们对于具有理想性质且无维增长的AH代数是等价的。然后给出了hausdorffation代数K1群可以从传统的Elliott不变量中恢复的充分条件。作为应用,一类具有理想性质、无维增长、有限多个理想的AH代数可以用扩展的Elliott不变量进行分类。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.
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
CiteScore
1.30
自引率
12.50%
发文量
23
审稿时长
12 months
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信