{"title":"论霍普夫图的莱维特路径代数","authors":"T. G. Nam, N. T. Phuc","doi":"10.1007/s40306-023-00511-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we provide the structure of Hopf graphs associated to pairs <span>\\((G, \\mathfrak {r})\\)</span> consisting of groups <i>G</i> together with ramification datas <span>\\(\\mathfrak {r}\\)</span> and their Leavitt path algebras. Consequently, we characterize the Gelfand-Kirillov dimension, the stable rank, the purely infinite simplicity and the existence of a nonzero finite dimensional representation of the Leavitt path algebra of a Hopf graph via properties of ramification data <span>\\(\\mathfrak {r}\\)</span> and <i>G</i>.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Leavitt Path Algebras of Hopf Graphs\",\"authors\":\"T. G. Nam, N. T. Phuc\",\"doi\":\"10.1007/s40306-023-00511-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we provide the structure of Hopf graphs associated to pairs <span>\\\\((G, \\\\mathfrak {r})\\\\)</span> consisting of groups <i>G</i> together with ramification datas <span>\\\\(\\\\mathfrak {r}\\\\)</span> and their Leavitt path algebras. Consequently, we characterize the Gelfand-Kirillov dimension, the stable rank, the purely infinite simplicity and the existence of a nonzero finite dimensional representation of the Leavitt path algebra of a Hopf graph via properties of ramification data <span>\\\\(\\\\mathfrak {r}\\\\)</span> and <i>G</i>.</p></div>\",\"PeriodicalId\":45527,\"journal\":{\"name\":\"Acta Mathematica Vietnamica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Vietnamica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40306-023-00511-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-023-00511-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在本文中,我们提供了霍普夫图的结构,该结构与由((G, \mathfrak {r})\)组成的群 G 及其斜分数据\(\mathfrak {r}\)和它们的 Leavitt 路径代数相关联。因此,我们通过斜切数据 \(\mathfrak {r}\) 和 G 的性质,描述了霍普夫图的 Leavitt 路径代数的格尔芬-基里洛夫维度、稳定秩、纯无限简单性和非零有限维表示的存在。
In this paper, we provide the structure of Hopf graphs associated to pairs \((G, \mathfrak {r})\) consisting of groups G together with ramification datas \(\mathfrak {r}\) and their Leavitt path algebras. Consequently, we characterize the Gelfand-Kirillov dimension, the stable rank, the purely infinite simplicity and the existence of a nonzero finite dimensional representation of the Leavitt path algebra of a Hopf graph via properties of ramification data \(\mathfrak {r}\) and G.
期刊介绍:
Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.