{"title":"Two \\(\\mathbb {Z}\\)-Graded Infinite Lie Conformal Algebras Related to the Virasoro Conformal Algebra","authors":"Xiaoqing Yue, Shun Zou","doi":"10.1007/s10468-024-10260-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study two <span>\\(\\mathbb {Z}\\)</span>-graded infinite Lie conformal algebras, which are closely related to a class of Lie algebras of the generalized Block type, and which both have a quotient algebra isomorphic to the Virasoro conformal algebra. We concretely determine their isomorphic mappings, conformal derivations, extensions by a one-dimensional center under some conditions, finite conformal modules and <span>\\(\\mathbb {Z}\\)</span>-graded free intermediate series modules.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-024-10260-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study two \(\mathbb {Z}\)-graded infinite Lie conformal algebras, which are closely related to a class of Lie algebras of the generalized Block type, and which both have a quotient algebra isomorphic to the Virasoro conformal algebra. We concretely determine their isomorphic mappings, conformal derivations, extensions by a one-dimensional center under some conditions, finite conformal modules and \(\mathbb {Z}\)-graded free intermediate series modules.
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