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Innovations in Incidence Geometry最新文献

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Affine buildings: construction by norms and study of isometries 仿射建筑:建筑规范和等距研究
Innovations in Incidence Geometry Pub Date : 2023-09-13 DOI: 10.2140/iig.2023.20.471
Anne Parreau
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引用次数: 3
The exceptional simple Lie group F4(−20), after J. Tits 异常单李群F4(−20)，后为J. Tits
Innovations in Incidence Geometry Pub Date : 2023-09-13 DOI: 10.2140/iig.2023.20.599
Alain J. Valette
{"title":"The exceptional simple Lie group F4(−20), after J. Tits","authors":"Alain J. Valette","doi":"10.2140/iig.2023.20.599","DOIUrl":"https://doi.org/10.2140/iig.2023.20.599","url":null,"abstract":"This is a semi-survey paper, where we start by advertising Tits' synthetic construction from cite{Tits}, of the hyperbolic plane $H^2(Cay)$ over the Cayley numbers $Cay$, and of its automorphism group which is the exceptional simple Lie group $G=F_{4(-20)}$. Let $G=KAN$ be the Iwasawa decomposition. Our contributions are: a) Writing down explicitly the action of $N$ on $H^2(Cay)$ in Tits'model, facing the lack of associativity of $Cay$. b) If $MAN$ denotes the minimal parabolic subgroup of $G$, characterizing $M$ geometrically.","PeriodicalId":36589,"journal":{"name":"Innovations in Incidence Geometry","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Locally projective graphs of symplectic type 辛型的局部投影图
Innovations in Incidence Geometry Pub Date : 2023-09-13 DOI: 10.2140/iig.2023.20.303
Alexander A. Ivanov
{"title":"Locally projective graphs of symplectic type","authors":"Alexander A. Ivanov","doi":"10.2140/iig.2023.20.303","DOIUrl":"https://doi.org/10.2140/iig.2023.20.303","url":null,"abstract":"","PeriodicalId":36589,"journal":{"name":"Innovations in Incidence Geometry","volume":"154 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135691542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Epimorphisms of generalized polygons, B: The octagons 广义多边形的外胚，B:八边形
Innovations in Incidence Geometry Pub Date : 2023-09-13 DOI: 10.2140/iig.2023.20.579
Joseph A. Thas, Koen Thas
{"title":"Epimorphisms of generalized polygons, B: The octagons","authors":"Joseph A. Thas, Koen Thas","doi":"10.2140/iig.2023.20.579","DOIUrl":"https://doi.org/10.2140/iig.2023.20.579","url":null,"abstract":"This is the second part of our study of epimorphisms with source a thick generalized $m$-gon and target a thin generalized $m$-gon. We classify the case $m = 8$ when the polygons are finite (in the first part [15] we handled the cases $m = 3, 4$ and $6$). Then we show that the infinite case is very different, and construct examples which strongly differ from the finite case. A number of general structure theorems are also obtained, and we also take a look at the infinite case for general gonality.","PeriodicalId":36589,"journal":{"name":"Innovations in Incidence Geometry","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134989790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Distances between fixed-point sets in metrically complete 2-dimensional Euclidean buildings are realised 实现了度量完备的二维欧几里得建筑中不动点集之间的距离
Innovations in Incidence Geometry Pub Date : 2023-09-13 DOI: 10.2140/iig.2023.20.341
Harris Leung, Jeroen Schillewaert, Anne Thomas
{"title":"Distances between fixed-point sets in metrically complete 2-dimensional Euclidean buildings are realised","authors":"Harris Leung, Jeroen Schillewaert, Anne Thomas","doi":"10.2140/iig.2023.20.341","DOIUrl":"https://doi.org/10.2140/iig.2023.20.341","url":null,"abstract":"","PeriodicalId":36589,"journal":{"name":"Innovations in Incidence Geometry","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Incidence geometries with trialities coming from maps with Wilson trialities 带有三角形的发生率几何来自带有威尔逊三角形的地图
Innovations in Incidence Geometry Pub Date : 2023-09-13 DOI: 10.2140/iig.2023.20.325
Dimitri Leemans, Klara Stokes
{"title":"Incidence geometries with trialities coming from maps with Wilson trialities","authors":"Dimitri Leemans, Klara Stokes","doi":"10.2140/iig.2023.20.325","DOIUrl":"https://doi.org/10.2140/iig.2023.20.325","url":null,"abstract":"Triality is a classical notion in geometry that arose in the context of the Lie groups of type $D_4$. Another notion of triality, Wilson triality, appears in the context of reflexible maps. We build a bridge between these two notions, showing how to construct an incidence geometry with a triality from a map that admits a Wilson triality. We also extend a result by Jones and Poulton, showing that for every prime power $q$, the group ${rm L}_2(q^3)$ has maps that admit Wilson trialities but no dualities.","PeriodicalId":36589,"journal":{"name":"Innovations in Incidence Geometry","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A geometric characterization of the symplectic Lie algebra 辛李代数的几何表征
Innovations in Incidence Geometry Pub Date : 2023-09-13 DOI: 10.2140/iig.2023.20.223
Hans Cuypers, Yael Fleischmann
{"title":"A geometric characterization of the symplectic Lie algebra","authors":"Hans Cuypers, Yael Fleischmann","doi":"10.2140/iig.2023.20.223","DOIUrl":"https://doi.org/10.2140/iig.2023.20.223","url":null,"abstract":"A nonzero element $x$ in a Lie algebra $mathfrak{g}$ with Lie product $[ , ]$ is called extremal if $[x,[x,y]]$ is a multiple of $x$ for all $y$. In this paper we characterize the (finitary) symplectic Lie algebras as simple Lie algebras generated by their extremal elements satisying the condition that any two noncommuting extremal elements $x,y$ generate an $mathfrak{sl}_2$ and any third extremal element $z$ commutes with at least one extremal element in this $mathfrak{sl}_2$.","PeriodicalId":36589,"journal":{"name":"Innovations in Incidence Geometry","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134990405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Chimney retractions in affine buildings encode orbits in affine flag varieties 仿射建筑物的烟囱缩回将轨道编码为仿射标志变体
Innovations in Incidence Geometry Pub Date : 2023-09-13 DOI: 10.2140/iig.2023.20.395
Elizabeth Milićević, Petra Schwer, Anne Thomas
{"title":"Chimney retractions in affine buildings encode orbits in affine flag varieties","authors":"Elizabeth Milićević, Petra Schwer, Anne Thomas","doi":"10.2140/iig.2023.20.395","DOIUrl":"https://doi.org/10.2140/iig.2023.20.395","url":null,"abstract":"This paper determines the relationship between the geometry of retractions and the combinatorics of folded galleries for arbitrary affine buildings, and so provides a unified framework to study orbits in affine flag varieties. We introduce the notion of labeled folded galleries for any affine building X and use these to describe the preimages of chimney retractions. When X is the building for a group with an affine Tits system, such as the Bruhat-Tits building for a group over a local field, we can then relate labeled folded galleries and shadows to double coset intersections in affine flag varieties. This result generalizes the authors' previous joint work with Naqvi on groups over function fields.","PeriodicalId":36589,"journal":{"name":"Innovations in Incidence Geometry","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Automorphisms and opposition in spherical buildings of exceptional type, II: Moufang hexagons 特殊类型球形建筑的自同构与对偶ⅱ:牟方六边形
Innovations in Incidence Geometry Pub Date : 2023-09-13 DOI: 10.2140/iig.2023.20.443
James Parkinson, Hendrik Van Maldeghem
{"title":"Automorphisms and opposition in spherical buildings of exceptional type, II: Moufang hexagons","authors":"James Parkinson, Hendrik Van Maldeghem","doi":"10.2140/iig.2023.20.443","DOIUrl":"https://doi.org/10.2140/iig.2023.20.443","url":null,"abstract":"We classify the automorphisms of a Moufang hexagon mapping no chamber to an opposite chamber (such automorphisms are called domestic). This forms part of a larger program to classify domestic automorphisms of Moufang spherical buildings.","PeriodicalId":36589,"journal":{"name":"Innovations in Incidence Geometry","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Rank three innately transitive permutation groups and related 2-transitive groups 对三个固有传递置换群和相关的2-传递群进行排序
Innovations in Incidence Geometry Pub Date : 2023-09-13 DOI: 10.2140/iig.2023.20.135
Anton A. Baykalov, Alice Devillers, Cheryl E. Praeger
{"title":"Rank three innately transitive permutation groups and related 2-transitive groups","authors":"Anton A. Baykalov, Alice Devillers, Cheryl E. Praeger","doi":"10.2140/iig.2023.20.135","DOIUrl":"https://doi.org/10.2140/iig.2023.20.135","url":null,"abstract":"The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analogues of composition factors for abstract finite groups. This paper extends classifications of finite primitive and quasiprimitive groups of rank at most $3$ to a classification for the finite innately transitive groups. The new examples comprise three infinite families and three sporadic examples. A necessary step in this classification was the determination of certain configurations in finite almost simple $2$-transitive groups called special pairs.","PeriodicalId":36589,"journal":{"name":"Innovations in Incidence Geometry","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135733598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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