{"title":"Non-weight modules over the super Schrödinger algebra","authors":"Xinyue Wang, Liangyun Chen, Yao Ma","doi":"10.21136/cmj.2024.0030-23","DOIUrl":null,"url":null,"abstract":"<p>We construct a family of non-weight modules which are free <span>\\(U(\\frak{h})\\)</span>-modules of rank 2 over the <i>N</i> = 1 super Schrödinger algebra in (1+1)-dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free <span>\\(U(\\frak{h})\\)</span>-modules of rank 2 over <span>\\(\\frak{osp}(1\\mid 2)\\)</span> are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Czechoslovak Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/cmj.2024.0030-23","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We construct a family of non-weight modules which are free \(U(\frak{h})\)-modules of rank 2 over the N = 1 super Schrödinger algebra in (1+1)-dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free \(U(\frak{h})\)-modules of rank 2 over \(\frak{osp}(1\mid 2)\) are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.
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