{"title":"量子格顶点代数的表示","authors":"Fei Kong","doi":"10.1016/j.jpaa.2024.107832","DOIUrl":null,"url":null,"abstract":"<div><div>Let <em>Q</em> be a non-degenerate even lattice, let <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow></msub></math></span> be the lattice vertex algebra associated to <em>Q</em>, and let <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow><mrow><mi>η</mi></mrow></msubsup></math></span> be a quantum lattice vertex algebra (<span><span>[10]</span></span>). In this paper, we prove that every <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow><mrow><mi>η</mi></mrow></msubsup></math></span>-module is completely reducible, and the set of simple <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow><mrow><mi>η</mi></mrow></msubsup></math></span>-modules are in one-to-one correspondence with the set of cosets of <em>Q</em> in its dual lattice.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Representations of quantum lattice vertex algebras\",\"authors\":\"Fei Kong\",\"doi\":\"10.1016/j.jpaa.2024.107832\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <em>Q</em> be a non-degenerate even lattice, let <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow></msub></math></span> be the lattice vertex algebra associated to <em>Q</em>, and let <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow><mrow><mi>η</mi></mrow></msubsup></math></span> be a quantum lattice vertex algebra (<span><span>[10]</span></span>). In this paper, we prove that every <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow><mrow><mi>η</mi></mrow></msubsup></math></span>-module is completely reducible, and the set of simple <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow><mrow><mi>η</mi></mrow></msubsup></math></span>-modules are in one-to-one correspondence with the set of cosets of <em>Q</em> in its dual lattice.</div></div>\",\"PeriodicalId\":54770,\"journal\":{\"name\":\"Journal of Pure and Applied Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-10-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pure and Applied Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022404924002299\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924002299","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Representations of quantum lattice vertex algebras
Let Q be a non-degenerate even lattice, let be the lattice vertex algebra associated to Q, and let be a quantum lattice vertex algebra ([10]). In this paper, we prove that every -module is completely reducible, and the set of simple -modules are in one-to-one correspondence with the set of cosets of Q in its dual lattice.
期刊介绍：
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.
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