{"title":"关于leavitt路径代数的exel effros-hahn猜想的分级版本","authors":"Loc Nguyen Quang, Ha Le Thi","doi":"10.18173/2354-1059.2022-0020","DOIUrl":null,"url":null,"abstract":"In this paper, we prove a graded version of Exel’s Effros-Hahn conjecture for Leavitt path algebras. More concretely, we show that any graded primitive ideal of the Leavitt path algebra is the annihilator of a module induced from a graded simple module over an isotropy group algebra. A graded version of Steinberg’s results towards Exel’s conjecture in (B. Steinberg, Ideals of etale ´groupoid algebras and Exel’s Effros-Hahn conjecture, J. Noncommut. Geom., Vol. 15, 2021, pp. 829-839) is also obtained for graded ample groupoid algebras.","PeriodicalId":17007,"journal":{"name":"Journal of Science Natural Science","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"GRADED VERSION OF EXEL’S EFFROS-HAHN CONJECTURE FOR LEAVITT PATH ALGEBRAS\",\"authors\":\"Loc Nguyen Quang, Ha Le Thi\",\"doi\":\"10.18173/2354-1059.2022-0020\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove a graded version of Exel’s Effros-Hahn conjecture for Leavitt path algebras. More concretely, we show that any graded primitive ideal of the Leavitt path algebra is the annihilator of a module induced from a graded simple module over an isotropy group algebra. A graded version of Steinberg’s results towards Exel’s conjecture in (B. Steinberg, Ideals of etale ´groupoid algebras and Exel’s Effros-Hahn conjecture, J. Noncommut. Geom., Vol. 15, 2021, pp. 829-839) is also obtained for graded ample groupoid algebras.\",\"PeriodicalId\":17007,\"journal\":{\"name\":\"Journal of Science Natural Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Science Natural Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18173/2354-1059.2022-0020\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Science Natural Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18173/2354-1059.2022-0020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
本文证明了Leavitt路径代数的Effros-Hahn猜想的一个分级版本。更具体地说，我们证明了Leavitt路径代数的任何梯度原始理想都是由各向同性群代数上的梯度单模导出的模的湮灭子。Steinberg对Exel猜想结果的一个分级版本(B. Steinberg，理想的类群代数和Exel的Effros-Hahn猜想，J. Noncommut)。几何学。， Vol. 15, 2021, pp. 829-839)也得到了分级样群代数。
GRADED VERSION OF EXEL’S EFFROS-HAHN CONJECTURE FOR LEAVITT PATH ALGEBRAS
In this paper, we prove a graded version of Exel’s Effros-Hahn conjecture for Leavitt path algebras. More concretely, we show that any graded primitive ideal of the Leavitt path algebra is the annihilator of a module induced from a graded simple module over an isotropy group algebra. A graded version of Steinberg’s results towards Exel’s conjecture in (B. Steinberg, Ideals of etale ´groupoid algebras and Exel’s Effros-Hahn conjecture, J. Noncommut. Geom., Vol. 15, 2021, pp. 829-839) is also obtained for graded ample groupoid algebras.
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