{"title":"A note on the Kleinewillinghöfer types of 4-dimensional Laguerre planes","authors":"G. Steinke","doi":"10.1515/advgeom-2022-0020","DOIUrl":null,"url":null,"abstract":"Abstract Kleinewillinghöfer classified in 1979 automorphism groups of Laguerre planes with respect to linearly transitive subgroups of central automorphisms and obtained a multitude of types. All feasible Kleinewillinghöfer types of 2-dimensional Laguerre planes were completely determined in 2021. In this paper we investigate the Kleinewillinghöfer types of 4-dimensional Laguerre planes with respect to the automorphism groups of these planes and show that of the 49 types Kleinewillinghöfer described, only twelve are feasible in 4-dimensional Laguerre planes. Examples of four of these type are provided.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/advgeom-2022-0020","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Abstract Kleinewillinghöfer classified in 1979 automorphism groups of Laguerre planes with respect to linearly transitive subgroups of central automorphisms and obtained a multitude of types. All feasible Kleinewillinghöfer types of 2-dimensional Laguerre planes were completely determined in 2021. In this paper we investigate the Kleinewillinghöfer types of 4-dimensional Laguerre planes with respect to the automorphism groups of these planes and show that of the 49 types Kleinewillinghöfer described, only twelve are feasible in 4-dimensional Laguerre planes. Examples of four of these type are provided.
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.
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