{"title":"Left-invariant distributions diffeomorphic to flat distributions","authors":"Sebastiano Nicolussi Golo, Alessandro Ottazzi","doi":"10.1007/s10711-024-00905-3","DOIUrl":null,"url":null,"abstract":"<p>For a stratified group <i>G</i>, we construct a class of Lie groups endowed with a left-invariant distribution locally diffeomorphic to the flat distribution of <i>G</i>. Vice versa, we show that all Lie groups with a left-invariant distribution that is locally diffeomorphic to the flat distribution of <i>G</i> belong to the class we constructed, if the Lie algebra of <i>G</i> has finite Tanaka prolongation.\n</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"10 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-03-13","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/s10711-024-00905-3","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
Abstract
For a stratified group G, we construct a class of Lie groups endowed with a left-invariant distribution locally diffeomorphic to the flat distribution of G. Vice versa, we show that all Lie groups with a left-invariant distribution that is locally diffeomorphic to the flat distribution of G belong to the class we constructed, if the Lie algebra of G has finite Tanaka prolongation.
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.
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