对称莱布尼兹代数的李论

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2019-10-05 DOI:10.1007/s40062-019-00248-x

Mamuka Jibladze, Teimuraz Pirashvili

{"title":"对称莱布尼兹代数的李论","authors":"Mamuka Jibladze, Teimuraz Pirashvili","doi":"10.1007/s40062-019-00248-x","DOIUrl":null,"url":null,"abstract":"Lie algebras and groups equipped with a multiplication \\(\\mu \\) satisfying some compatibility properties are studied. These structures are called symmetric Lie \\(\\mu \\)-algebras and symmetric \\(\\mu \\)-groups respectively. An equivalence of categories between symmetric Lie \\(\\mu \\)-algebras and symmetric Leibniz algebras is established when 2 is invertible in the base ring. The second main result of the paper is an equivalence of categories between simply connected symmetric Lie \\(\\mu \\)-groups and finite dimensional symmetric Leibniz algebras.","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"15 1","pages":"167 - 183"},"PeriodicalIF":0.5000,"publicationDate":"2019-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-019-00248-x","citationCount":"1","resultStr":"{\"title\":\"Lie theory for symmetric Leibniz algebras\",\"authors\":\"Mamuka Jibladze, Teimuraz Pirashvili\",\"doi\":\"10.1007/s40062-019-00248-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Lie algebras and groups equipped with a multiplication \\\\(\\\\mu \\\\) satisfying some compatibility properties are studied. These structures are called symmetric Lie \\\\(\\\\mu \\\\)-algebras and symmetric \\\\(\\\\mu \\\\)-groups respectively. An equivalence of categories between symmetric Lie \\\\(\\\\mu \\\\)-algebras and symmetric Leibniz algebras is established when 2 is invertible in the base ring. The second main result of the paper is an equivalence of categories between simply connected symmetric Lie \\\\(\\\\mu \\\\)-groups and finite dimensional symmetric Leibniz algebras.\",\"PeriodicalId\":636,\"journal\":{\"name\":\"Journal of Homotopy and Related Structures\",\"volume\":\"15 1\",\"pages\":\"167 - 183\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2019-10-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40062-019-00248-x\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Homotopy and Related Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-019-00248-x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"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/s40062-019-00248-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

研究了具有满足相容性的乘法\(\mu \)的李代数和李群。这些结构分别称为对称李氏\(\mu \) -代数和对称\(\mu \) -群。当2在基环上可逆时，建立了对称Lie代数\(\mu \) -代数与对称Leibniz代数之间的范畴等价。本文的第二个主要结果是单连通对称李\(\mu \) -群与有限维对称莱布尼兹代数之间的范畴等价。

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 theory for symmetric Leibniz algebras

Lie algebras and groups equipped with a multiplication \(\mu \) satisfying some compatibility properties are studied. These structures are called symmetric Lie \(\mu \)-algebras and symmetric \(\mu \)-groups respectively. An equivalence of categories between symmetric Lie \(\mu \)-algebras and symmetric Leibniz algebras is established when 2 is invertible in the base ring. The second main result of the paper is an equivalence of categories between simply connected symmetric Lie \(\mu \)-groups and finite dimensional symmetric Leibniz algebras.

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-Geometry and Topology

自引率

0.00%

发文量

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.