{"title":"A new axiomatics for masures II","authors":"Auguste Hébert","doi":"10.1515/advgeom-2022-0013","DOIUrl":null,"url":null,"abstract":"Abstract Masures are generalizations of Bruhat–Tits buildings. They were introduced by Gaussent and Rousseau in order to study Kac–Moody groups over valued fields. We prove that the intersection of two apartments of a masure is convex. Using this, we simplify the axiomatic definition of masures given by Rousseau.","PeriodicalId":7335,"journal":{"name":"Advances in Geometry","volume":"22 1","pages":"513 - 522"},"PeriodicalIF":0.5000,"publicationDate":"2021-01-14","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-2022-0013","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
Abstract
Abstract Masures are generalizations of Bruhat–Tits buildings. They were introduced by Gaussent and Rousseau in order to study Kac–Moody groups over valued fields. We prove that the intersection of two apartments of a masure is convex. Using this, we simplify the axiomatic definition of masures given by Rousseau.
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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