{"title":"Classifying Recollements of Derived Module Categories for Derived Discrete Algebras","authors":"Xiuli Bian","doi":"10.1007/s10468-023-10220-2","DOIUrl":null,"url":null,"abstract":"<div><p>We study a class of derived discrete Nakayama algebras. All indecomposable compact objects in the derived module category are determined and all recollements generated by the indecomposable compact exceptional objects are classified. It reveals that all such recollements are derived equivalent to stratifying recollements. As a byproduct, this confirms a question due to Xi for these recollements.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 1","pages":"279 - 304"},"PeriodicalIF":0.5000,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebras and Representation Theory","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-023-10220-2","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
Abstract
We study a class of derived discrete Nakayama algebras. All indecomposable compact objects in the derived module category are determined and all recollements generated by the indecomposable compact exceptional objects are classified. It reveals that all such recollements are derived equivalent to stratifying recollements. As a byproduct, this confirms a question due to Xi for these recollements.
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.
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