{"title":"超薛定谔代数上的非重模块","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.21136/cmj.2024.0030-23\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/cmj.2024.0030-23","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Non-weight modules over the super Schrödinger algebra
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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