束根和库朗梯形的无限对称性

IF 0.5 4区数学 Q3 MATHEMATICS Geometriae Dedicata 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":55103,"journal":{"name":"Geometriae Dedicata","volume":"2015 1","pages":""},"PeriodicalIF":0.5000,"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\":55103,\"journal\":{\"name\":\"Geometriae Dedicata\",\"volume\":\"2015 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-02-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometriae Dedicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10711-024-00897-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometriae Dedicata","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10711-024-00897-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","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

本刊更多论文

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

来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.

期刊最新文献

Coarse entropy of metric spaces Geodesic vector fields, induced contact structures and tightness in dimension three Key varieties for prime $$\pmb {\mathbb {Q}}$$ -Fano threefolds defined by Freudenthal triple systems Stable vector bundles on fibered threefolds over a surface Fundamental regions for non-isometric group actions