派生发展水平的对称性

IF 0.6 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-08-01 DOI:10.1007/s10468-025-10355-4

Ruoyu Guo

{"title":"派生发展水平的对称性","authors":"Ruoyu Guo","doi":"10.1007/s10468-025-10355-4","DOIUrl":null,"url":null,"abstract":"<div><p>The finitistic dimension conjecture is closely connected to the symmetry of the finitistic dimension. Recent work indicates that such connection extends to one of its upper bounds, the delooping level. In this paper, we show that the same holds for the derived delooping level, which is an improvement of the delooping level. This reduces the finitistic dimension conjecture to considering algebras whose opposite algebra has (derived) delooping level zero. We thereby demonstrate ways to utilize the new concept of derived delooping level to obtain new results and present additional work involving tensor product of algebras.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 4","pages":"1125 - 1137"},"PeriodicalIF":0.6000,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10355-4.pdf","citationCount":"0","resultStr":"{\"title\":\"Symmetry of Derived Delooping Level\",\"authors\":\"Ruoyu Guo\",\"doi\":\"10.1007/s10468-025-10355-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The finitistic dimension conjecture is closely connected to the symmetry of the finitistic dimension. Recent work indicates that such connection extends to one of its upper bounds, the delooping level. In this paper, we show that the same holds for the derived delooping level, which is an improvement of the delooping level. This reduces the finitistic dimension conjecture to considering algebras whose opposite algebra has (derived) delooping level zero. We thereby demonstrate ways to utilize the new concept of derived delooping level to obtain new results and present additional work involving tensor product of algebras.</p></div>\",\"PeriodicalId\":50825,\"journal\":{\"name\":\"Algebras and Representation Theory\",\"volume\":\"28 4\",\"pages\":\"1125 - 1137\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2025-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10468-025-10355-4.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebras and Representation Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10468-025-10355-4\",\"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":"Algebras and Representation Theory","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-025-10355-4","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

有限维猜想与有限维的对称性密切相关。最近的研究表明，这种联系延伸到它的一个上界，即发展水平。在本文中，我们证明了导出的开发水平也是如此，它是开发水平的改进。这将有限维猜想简化为考虑其对代数（推导）的发展水平为零的代数。因此，我们展示了如何利用派生发展水平的新概念来获得新的结果，并提出了涉及代数张量积的额外工作。

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

Symmetry of Derived Delooping Level

The finitistic dimension conjecture is closely connected to the symmetry of the finitistic dimension. Recent work indicates that such connection extends to one of its upper bounds, the delooping level. In this paper, we show that the same holds for the derived delooping level, which is an improvement of the delooping level. This reduces the finitistic dimension conjecture to considering algebras whose opposite algebra has (derived) delooping level zero. We thereby demonstrate ways to utilize the new concept of derived delooping level to obtain new results and present additional work involving tensor product of algebras.

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

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.