关于利玛窦的负推导

IF 0.5 4区 数学 Q3 MATHEMATICS
María Valeria Gutiérrez
{"title":"关于利玛窦的负推导","authors":"María Valeria Gutiérrez","doi":"10.1515/advgeom-2022-0004","DOIUrl":null,"url":null,"abstract":"Abstract Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. Lauret and Will have conjectured that such a space coincides with an open and convex subset of derivations defined in terms of the moment map for the variety of nilpotent Lie algebras. We prove the validity of the conjecture in dimensions ≤ 5, as well as for Heisenberg Lie algebras and standard filiform Lie algebras.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2020-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On Ricci negative derivations\",\"authors\":\"María Valeria Gutiérrez\",\"doi\":\"10.1515/advgeom-2022-0004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. Lauret and Will have conjectured that such a space coincides with an open and convex subset of derivations defined in terms of the moment map for the variety of nilpotent Lie algebras. We prove the validity of the conjecture in dimensions ≤ 5, as well as for Heisenberg Lie algebras and standard filiform Lie algebras.\",\"PeriodicalId\":7335,\"journal\":{\"name\":\"Advances in Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-12-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/advgeom-2022-0004\",\"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":"Advances in Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/advgeom-2022-0004","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: 1

摘要

摘要给定一个幂零李代数,研究了所有可对角导的空间,使得相应的一维可解扩展允许一个负Ricci曲率的左不变度量。Lauret和Will推测这样的空间与幂零李代数的矩映射定义的导数的开凸子集相吻合。我们证明了这个猜想在维数≤5上的有效性,以及对于Heisenberg李代数和标准丝状李代数的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On Ricci negative derivations
Abstract Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. Lauret and Will have conjectured that such a space coincides with an open and convex subset of derivations defined in terms of the moment map for the variety of nilpotent Lie algebras. We prove the validity of the conjecture in dimensions ≤ 5, as well as for Heisenberg Lie algebras and standard filiform Lie 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
Advances in Geometry
Advances in Geometry 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
31
审稿时长
>12 weeks
期刊介绍: Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信