{"title":"单项式代数的三维扩展是 S 型对称分数布劳尔构型代数","authors":"Yuming Liu, Bohan Xing","doi":"arxiv-2408.02537","DOIUrl":null,"url":null,"abstract":"By giving some equivalent definitions of fractional Brauer configuration\nalgebras of type S in some special cases, we construct a fractional Brauer\nconfiguration from any monomial algebra. We show that this algebra is\nisomorphic to the trivial extension of the given monomial algebra. Moreover, we\nshow that there exists a one-to-one correspondence between the isomorphism\nclasses of monomial algebras and the equivalence classes of pairs consisting of\na symmetric fractional Brauer configuration algebra of type S with trivial\ndegree function and a given admissible cut over it.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"60 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras of type S\",\"authors\":\"Yuming Liu, Bohan Xing\",\"doi\":\"arxiv-2408.02537\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"By giving some equivalent definitions of fractional Brauer configuration\\nalgebras of type S in some special cases, we construct a fractional Brauer\\nconfiguration from any monomial algebra. We show that this algebra is\\nisomorphic to the trivial extension of the given monomial algebra. Moreover, we\\nshow that there exists a one-to-one correspondence between the isomorphism\\nclasses of monomial algebras and the equivalence classes of pairs consisting of\\na symmetric fractional Brauer configuration algebra of type S with trivial\\ndegree function and a given admissible cut over it.\",\"PeriodicalId\":501136,\"journal\":{\"name\":\"arXiv - MATH - Rings and Algebras\",\"volume\":\"60 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Rings and Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.02537\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.02537","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
通过给出一些特殊情况下 S 型分数布劳尔配置体的等价定义,我们从任何单项式代数中构造出一个分数布劳尔配置体。我们证明,这个代数与给定单项式代数的微不足道的扩展同构。此外,我们还证明了单项式代数的同构类与由具有三阶度函数的 S 型对称分数布劳尔配置代数和在其上的给定容许割组成的对的等价类之间存在一一对应关系。
Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras of type S
By giving some equivalent definitions of fractional Brauer configuration
algebras of type S in some special cases, we construct a fractional Brauer
configuration from any monomial algebra. We show that this algebra is
isomorphic to the trivial extension of the given monomial algebra. Moreover, we
show that there exists a one-to-one correspondence between the isomorphism
classes of monomial algebras and the equivalence classes of pairs consisting of
a symmetric fractional Brauer configuration algebra of type S with trivial
degree function and a given admissible cut over it.