束根和库朗梯形的无限对称性

Pub Date : 2024-02-26 DOI:10.1007/s10711-024-00897-0

{"title":"束根和库朗梯形的无限对称性","authors":"","doi":"10.1007/s10711-024-00897-0","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> Let M be a smooth manifold and let \\(\\chi \\in \\Omega ^3(M)\\) be closed differential form with integral periods. We show the Lie 2-algebra \\(\\mathbb {L}(C_\\chi )\\) of sections of the \\(\\chi \\) -twisted Courant algebroid \\(C_\\chi \\) on M is quasi-isomorphic to the Lie 2-algebra of connection-preserving multiplicative vector fields on an \\(S^1\\) -bundle gerbe with connection (over M) whose 3-curvature is \\(\\chi \\) . ","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Infinitesimal symmetries of bundle gerbes and Courant algebroids\",\"authors\":\"\",\"doi\":\"10.1007/s10711-024-00897-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> Let M be a smooth manifold and let \\\\(\\\\chi \\\\in \\\\Omega ^3(M)\\\\) be closed differential form with integral periods. We show the Lie 2-algebra \\\\(\\\\mathbb {L}(C_\\\\chi )\\\\) of sections of the \\\\(\\\\chi \\\\) -twisted Courant algebroid \\\\(C_\\\\chi \\\\) on M is quasi-isomorphic to the Lie 2-algebra of connection-preserving multiplicative vector fields on an \\\\(S^1\\\\) -bundle gerbe with connection (over M) whose 3-curvature is \\\\(\\\\chi \\\\) . \",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-02-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10711-024-00897-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10711-024-00897-0","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

Abstract Let M be a smooth manifold and let \(\chi \in \Omega ^3(M)\) be closed differential form with integral periods.我们证明在M上的\(\chi \) -twisted Courant algebroid \(C_\chi \)的截面的Lie 2-代数（\mathbb {L}(C_\chi )）与3-曲率为\(\chi \)的\(S^1\) -bundle gerbe with connection (over M)上的连接保留乘法向量场的Lie 2-代数准同构。

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

微信好友朋友圈 QQ好友复制链接

Infinitesimal symmetries of bundle gerbes and Courant algebroids

Abstract

Let M be a smooth manifold and let \(\chi \in \Omega ^3(M)\) be closed differential form with integral periods. We show the Lie 2-algebra \(\mathbb {L}(C_\chi )\) of sections of the \(\chi \) -twisted Courant algebroid \(C_\chi \) on M is quasi-isomorphic to the Lie 2-algebra of connection-preserving multiplicative vector fields on an \(S^1\) -bundle gerbe with connection (over M) whose 3-curvature is \(\chi \) .

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