{"title":"平面伽利略型有限Lie共形布尔上的共形模数扩展","authors":"Xiu Han, Dengyin Wang, Chunguang Xia","doi":"10.1016/S0034-4877(24)00077-6","DOIUrl":null,"url":null,"abstract":"<div><div>We classify extensions between finite irreducible conformal modules over Lie conformal algebras <strong>B</strong>ℌ(<em>a, b)</em> of planar Galilean type, where <em>a</em> and <em>b</em> are complex numbers. We find that although finite irreducible conformal modules over <strong>B</strong>ℌ(<em>a</em>, <em>b)</em> are simply conformal modules over its Heisenberg–Virasoro conformal subalgebra, there exist more nontrivial extensions between conformal <strong>B</strong>ℌ(<em>a, b</em>)-modules.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 2","pages":"Pages 219-233"},"PeriodicalIF":1.0000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Extensions of Conformal Modules Over Finite Lie Conformal Algebras of Planar Galilean Type\",\"authors\":\"Xiu Han, Dengyin Wang, Chunguang Xia\",\"doi\":\"10.1016/S0034-4877(24)00077-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We classify extensions between finite irreducible conformal modules over Lie conformal algebras <strong>B</strong>ℌ(<em>a, b)</em> of planar Galilean type, where <em>a</em> and <em>b</em> are complex numbers. We find that although finite irreducible conformal modules over <strong>B</strong>ℌ(<em>a</em>, <em>b)</em> are simply conformal modules over its Heisenberg–Virasoro conformal subalgebra, there exist more nontrivial extensions between conformal <strong>B</strong>ℌ(<em>a, b</em>)-modules.</div></div>\",\"PeriodicalId\":49630,\"journal\":{\"name\":\"Reports on Mathematical Physics\",\"volume\":\"94 2\",\"pages\":\"Pages 219-233\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Reports on Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0034487724000776\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000776","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
摘要
我们对平面伽利略类型的 Lie 共形代数 Bℌ(a,b)上的有限不可还原共形模块之间的扩展进行了分类，其中 a 和 b 是复数。我们发现，虽然 Bℌ(a,b)上的有限不可还原共形模块只是其 Heisenberg-Virasoro 共形子代数上的共形模块，但 Bℌ(a,b)共形模块之间存在更多的非难扩展。
Extensions of Conformal Modules Over Finite Lie Conformal Algebras of Planar Galilean Type
We classify extensions between finite irreducible conformal modules over Lie conformal algebras Bℌ(a, b) of planar Galilean type, where a and b are complex numbers. We find that although finite irreducible conformal modules over Bℌ(a, b) are simply conformal modules over its Heisenberg–Virasoro conformal subalgebra, there exist more nontrivial extensions between conformal Bℌ(a, b)-modules.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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