{"title":"Cocommutative connected vertex (operator) bialgebras","authors":"Yukun Xiao , Jianzhi Han","doi":"10.1016/j.geomphys.2025.105461","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, by the equivalence between the category of Lie conformal algebras and the category of cocommutative connected vertex bialgebras, which was obtained in <span><span>[8]</span></span>, we classify simple objects in the latter category. We introduce the notion of Lie conformal operator algebra and the notion of vertex operator bialgebra. And it is shown that the category of Lie conformal operator algebras and the category of cocommutative connected vertex operator bialgebras are equivalent.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"212 ","pages":"Article 105461"},"PeriodicalIF":1.6000,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geometry and Physics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0393044025000452","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, by the equivalence between the category of Lie conformal algebras and the category of cocommutative connected vertex bialgebras, which was obtained in [8], we classify simple objects in the latter category. We introduce the notion of Lie conformal operator algebra and the notion of vertex operator bialgebra. And it is shown that the category of Lie conformal operator algebras and the category of cocommutative connected vertex operator bialgebras are equivalent.
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The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields.
The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered.
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