来自环群扩展的李2群

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2024-09-26 DOI:10.1007/s40062-024-00355-4

Matthias Ludewig, Konrad Waldorf

{"title":"来自环群扩展的李2群","authors":"Matthias Ludewig, Konrad Waldorf","doi":"10.1007/s40062-024-00355-4","DOIUrl":null,"url":null,"abstract":"<div><p>We give a very simple construction of the string 2-group as a strict Fréchet Lie 2-group. The corresponding crossed module is defined using the conjugation action of the loop group on its central extension, which drastically simplifies several constructions previously given in the literature. More generally, we construct strict 2-group extensions for a Lie group from a central extension of its based loop group, under the assumption that this central extension is disjoint commutative. We show in particular that this condition is automatic in the case that the Lie group is semisimple and simply connected.</p></div>","PeriodicalId":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"19 4","pages":"597 - 633"},"PeriodicalIF":0.7000,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40062-024-00355-4.pdf","citationCount":"0","resultStr":"{\"title\":\"Lie 2-groups from loop group extensions\",\"authors\":\"Matthias Ludewig, Konrad Waldorf\",\"doi\":\"10.1007/s40062-024-00355-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We give a very simple construction of the string 2-group as a strict Fréchet Lie 2-group. The corresponding crossed module is defined using the conjugation action of the loop group on its central extension, which drastically simplifies several constructions previously given in the literature. More generally, we construct strict 2-group extensions for a Lie group from a central extension of its based loop group, under the assumption that this central extension is disjoint commutative. We show in particular that this condition is automatic in the case that the Lie group is semisimple and simply connected.</p></div>\",\"PeriodicalId\":49034,\"journal\":{\"name\":\"Journal of Homotopy and Related Structures\",\"volume\":\"19 4\",\"pages\":\"597 - 633\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-09-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40062-024-00355-4.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Homotopy and Related Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-024-00355-4\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-024-00355-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们给出了弦 2 群作为严格弗雷谢特列 2 群的一个非常简单的构造。相应的交叉模块是利用环群对其中心外延的共轭作用定义的，这大大简化了之前文献中给出的一些构造。更一般地说，我们从基于环群的中心外延出发，为一个李群构造严格的 2 群外延，前提是这个中心外延是不相交的。我们特别证明，在李群是半简单和简单连接的情况下，这一条件是自动的。

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

Lie 2-groups from loop group extensions

We give a very simple construction of the string 2-group as a strict Fréchet Lie 2-group. The corresponding crossed module is defined using the conjugation action of the loop group on its central extension, which drastically simplifies several constructions previously given in the literature. More generally, we construct strict 2-group extensions for a Lie group from a central extension of its based loop group, under the assumption that this central extension is disjoint commutative. We show in particular that this condition is automatic in the case that the Lie group is semisimple and simply connected.

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

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.