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Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial最新文献

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Géométrie de l’espace, du temps et de lacausalité : la voie axiomatique 空间、时间和多样性的几何学:公理路径
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial Pub Date : 2018-12-31 DOI: 10.2140/IIG.2018.16.245
J. Tits
{"title":"Géométrie de l’espace, du temps et de la\u0000causalité : la voie axiomatique","authors":"J. Tits","doi":"10.2140/IIG.2018.16.245","DOIUrl":"https://doi.org/10.2140/IIG.2018.16.245","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":" 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113948604","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
Sur les groupes algébriques affins :théorèmes fondamentaux de structure ; classification des groupes semisimples etgéométries associées 仿射代数群:基本结构定理;半简单群和相关几何群的分类
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial Pub Date : 2018-12-31 DOI: 10.2140/iig.2018.16.79
J. Tits
{"title":"Sur les groupes algébriques affins :\u0000théorèmes fondamentaux de structure ; classification des groupes semisimples et\u0000géométries associées","authors":"J. Tits","doi":"10.2140/iig.2018.16.79","DOIUrl":"https://doi.org/10.2140/iig.2018.16.79","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"292 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133380086","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
Étude de certains espaces métriques 某些度量空间的研究
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial Pub Date : 2018-12-31 DOI: 10.2140/IIG.2018.16.37
J. Tits
{"title":"Étude de certains espaces métriques","authors":"J. Tits","doi":"10.2140/IIG.2018.16.37","DOIUrl":"https://doi.org/10.2140/IIG.2018.16.37","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"86 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121009297","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: 3
Symétries 对称度
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial Pub Date : 2018-12-31 DOI: 10.2140/iig.2018.16.267
Jacques Tits
{"title":"Symétries","authors":"Jacques Tits","doi":"10.2140/iig.2018.16.267","DOIUrl":"https://doi.org/10.2140/iig.2018.16.267","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129373468","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
Sur un article précédent : « Étude decertains espaces métriques » 在之前的一篇文章中:《某些度量空间的研究》
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial Pub Date : 2018-12-31 DOI: 10.2140/iig.2018.16.47
J. Tits
{"title":"Sur un article précédent : « Étude de\u0000certains espaces métriques »","authors":"J. Tits","doi":"10.2140/iig.2018.16.47","DOIUrl":"https://doi.org/10.2140/iig.2018.16.47","url":null,"abstract":"","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132493629","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
On two nonbuilding but simply connectedcompact Tits geometries of type C3 在两个非建筑但简单连接的紧凑的C3型几何上
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial Pub Date : 2018-11-12 DOI: 10.2140/iig.2019.17.221
A. Pasini
{"title":"On two nonbuilding but simply connected\u0000compact Tits geometries of type C3","authors":"A. Pasini","doi":"10.2140/iig.2019.17.221","DOIUrl":"https://doi.org/10.2140/iig.2019.17.221","url":null,"abstract":"A classification of homogeneous compact Tits geometries of irreducible spherical type, with connected panels and admitting a compact flag-transitive automorphism group acting continuously on the geometry, has been obtained by Kramer and Lytchak (Homogeneous compact geometries, Transform. Groups 19 (2016), 43-58 and Erratum to: Homogeneous compact geometries, Transform. Groups, to appear). According to their main result, all such geometries but two are quotients of buildings. The two exceptions are flat geometries of type C3 and arise from polar actions on the Cayley plane over the division algebra of real octonions. The classification obtained by Kramer and Lytchak does not contain the claim that those two exceptional geometries are simply connected, but this holds true, as proved by Schillewaert and Struyve (On exceptional homogeneous compact geometries of type C3, Groups Geome. Dyn. 11 (2017), 1377-1399). The proof by Schillewaert and Struyve is of topological nature and relies on the main result of Kramer and Lytchak. In this paper we provide a combinatorial proof of that claim, independent of Kramer and Lytchak's result.","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"08 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125700404","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
Opposition diagrams for automorphisms of small spherical buildings 小型球形建筑自同构的对偶图
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial Pub Date : 2018-03-25 DOI: 10.2140/iig.2019.17.141
J. Parkinson, H. Maldeghem
{"title":"Opposition diagrams for automorphisms of small spherical buildings","authors":"J. Parkinson, H. Maldeghem","doi":"10.2140/iig.2019.17.141","DOIUrl":"https://doi.org/10.2140/iig.2019.17.141","url":null,"abstract":"An automorphism $theta$ of a spherical building $Delta$ is called textit{capped} if it satisfies the following property: if there exist both type $J_1$ and $J_2$ simplices of $Delta$ mapped onto opposite simplices by $theta$ then there exists a type $J_1cup J_2$ simplex of $Delta$ mapped onto an opposite simplex by $theta$. In previous work we showed that if $Delta$ is a thick irreducible spherical building of rank at least $3$ with no Fano plane residues then every automorphism of $Delta$ is capped. In the present work we consider the spherical buildings with Fano plane residues (the textit{small buildings}). We show that uncapped automorphisms exist in these buildings and develop an enhanced notion of \"opposition diagrams\" to capture the structure of these automorphisms. Moreover we provide applications to the theory of \"domesticity\" in spherical buildings, including the complete classification of domestic automorphisms of small buildings of types $mathsf{F}_4$ and $mathsf{E}_6$.","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124523818","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: 4
Regular pseudo-hyperovals and regular pseudo-ovals in even characteristic 正则伪超卵圆和偶特征的正则伪卵圆
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial Pub Date : 2017-01-31 DOI: 10.2140/iig.2019.17.77
J. Thas
{"title":"Regular pseudo-hyperovals and regular pseudo-ovals in even characteristic","authors":"J. Thas","doi":"10.2140/iig.2019.17.77","DOIUrl":"https://doi.org/10.2140/iig.2019.17.77","url":null,"abstract":"S. Rottey and G. Van de Voorde characterized regular pseudo-ovals of PG(3n - 1, q), q = 2^h, h >1 and n prime. Here an alternative proof is given and slightly stronger results are obtained.","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"338 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116445562","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
On triples of ideal chambers inA2-buildings 在2楼理想房间的三倍上
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial Pub Date : 2015-04-01 DOI: 10.2140/iig.2019.17.109
A. Parreau
{"title":"On triples of ideal chambers in\u0000A2-buildings","authors":"A. Parreau","doi":"10.2140/iig.2019.17.109","DOIUrl":"https://doi.org/10.2140/iig.2019.17.109","url":null,"abstract":"We investigate the geometry in a real Euclidean building X of type A2 of some simple configurations in the associated projective plane at infinity P, seen as ideal configurations in X, and relate it with the projective invariants (from the cross ratio on P). In particular we establish a geometric classification of generic triples of ideal chambers of X and relate it with the triple ratio of triples of flags.","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132619007","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: 3
The exterior splash in PG(6,q) :transversals PG(6,q)的外部飞溅:横截面
Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial Pub Date : 2014-09-24 DOI: 10.2140/IIG.2019.17.1
S. G. Barwick, Wen-Ai Jackson
{"title":"The exterior splash in PG(6,q) :\u0000transversals","authors":"S. G. Barwick, Wen-Ai Jackson","doi":"10.2140/IIG.2019.17.1","DOIUrl":"https://doi.org/10.2140/IIG.2019.17.1","url":null,"abstract":"Let $pi$ be an order-$q$-subplane of $PG(2,q^3)$ that is exterior to $ell_infty$. Then the exterior splash of $pi$ is the set of $q^2+q+1$ points on $ell_infty$ that lie on an extended line of $pi$. Exterior splashes are projectively equivalent to scattered linear sets of rank 3, covers of the circle geometry $CG(3,q)$, and hyper-reguli in $PG(5,q)$. In this article we use the Bruck-Bose representation in $PG(6,q)$ to investigate the structure of $pi$, and the interaction between $pi$ and its exterior splash. In $PG(6,q)$, an exterior splash $mathbb S$ has two sets of cover planes (which are hyper-reguli) and we show that each set has three unique transversals lines in the cubic extension $PG(6,q^3)$. These transversal lines are used to characterise the carriers of $mathbb S$, and to characterise the sublines of $mathbb S$.","PeriodicalId":127937,"journal":{"name":"Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131054920","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
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