群形半直接积落束II——主要作用及其稳定性

IF 1.2 2区数学 Q1 MATHEMATICS

Indiana University Mathematics Journal Pub Date : 2021-05-05 DOI:10.1512/iumj.2023.72.9447

Lucas Hall, S. Kaliszewski, John Quigg, Dana P. Williams

{"title":"群形半直接积落束II——主要作用及其稳定性","authors":"Lucas Hall, S. Kaliszewski, John Quigg, Dana P. Williams","doi":"10.1512/iumj.2023.72.9447","DOIUrl":null,"url":null,"abstract":"Given a free and proper action of a groupoid on a Fell bundle (over another groupoid), we give an equivalence between the semidirect-product and the generalized-fixed-point Fell bundles, generalizing an earlier result where the action was by a group. As an application, we show that the Stabilization Theorem for Fell bundles over groupoids is essentially another form of crossed-product duality.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2021-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Groupoid semidirect product Fell bundles II --- principal actions and stabilization\",\"authors\":\"Lucas Hall, S. Kaliszewski, John Quigg, Dana P. Williams\",\"doi\":\"10.1512/iumj.2023.72.9447\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a free and proper action of a groupoid on a Fell bundle (over another groupoid), we give an equivalence between the semidirect-product and the generalized-fixed-point Fell bundles, generalizing an earlier result where the action was by a group. As an application, we show that the Stabilization Theorem for Fell bundles over groupoids is essentially another form of crossed-product duality.\",\"PeriodicalId\":50369,\"journal\":{\"name\":\"Indiana University Mathematics Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2021-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indiana University Mathematics Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1512/iumj.2023.72.9447\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indiana University Mathematics Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1512/iumj.2023.72.9447","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

给出了群类群在Fell束上(在另一个群类群上)的自由和固有作用，给出了半直积和广义不动点Fell束之间的等价，推广了先前的结果，其中作用是由群产生的。作为一个应用，我们证明了群类群上落束的镇定定理实质上是另一种形式的叉积对偶。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Groupoid semidirect product Fell bundles II --- principal actions and stabilization

Given a free and proper action of a groupoid on a Fell bundle (over another groupoid), we give an equivalence between the semidirect-product and the generalized-fixed-point Fell bundles, generalizing an earlier result where the action was by a group. As an application, we show that the Stabilization Theorem for Fell bundles over groupoids is essentially another form of crossed-product duality.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊