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In der Mathematik sind Bruhat-Tits-Gebäude eine nicht-archimedische Variante symmetrischer Räume. Sie sind nach François Bruhat und Jacques Tits benannt. (de) In mathematics, a building (also Tits building, named after Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces. Buildings were initially introduced by Jacques Tits as a means to understand the structure of exceptional groups of Lie type. The more specialized theory of Bruhat–Tits buildings (named also after François Bruhat) plays a role in the study of p-adic Lie groups analogous to that of the theory of symmetric spaces in the theory of Lie groups. (en) En mathématiques, un immeuble, aussi appelé l’immeuble Tits et l’immeuble Bruhat-Tits (nommé d'après François Bruhat et Jacques Tits) est une structure combinatoire et géométrique qui généralise simultanément certains aspects des variétés de drapeaux, des plans projectifs finis, et les espaces riemanniens symétriques. Introduite par Jacques Tits comme moyen de comprendre la structure des groupes exceptionnels de type de Lie, la théorie a également été utilisée pour l'étude de la géométrie et de la topologie des espaces homogènes des et leurs sous-groupes de symétrie discrets, de la même manière que les arbres ont été utilisés pour étudier les groupes libres. (fr) 数学における（ティッツの、あるいはブリュア–ティッツの）建物（たてもの、英: building, 仏: immeuble）は、とジャック・ティッツに名を因む、旗多様体、有限射影平面およびのある種の側面を一斉に一般化する組合せ論的かつ幾何学的な構造である。初め、建物はジャック・ティッツによっての構造を理解するための手段として導入され、その理論は自由群の研究に木が用いられたのと同じ仕方で、その離散的対称変換部分群の等質空間の幾何および位相を研究するのにも用いられた。 (ja) |
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http://web.univ-ubs.fr/lmam/barre/henri.pdf%7Cdoi=10.1007/s10711-007-9206-0 http://www.numdam.org/item%3Fid=PMIHES_1972__41__5_0%7Cdoi= http://www.numdam.org/item%3Fid=PMIHES_1995__82__169_0%7Cdoi=10.1007/bf02698640%7Cciteseerx=10.1.1.30.8282 http://www.numdam.org/numdam-bin/fitem%3Fid=AIF_1995__45_4_1037_0%7Cdoi=10.5802/aif.1483%7Caccess-date=2008-01-03%7Carchive-url=https:/web.archive.org/web/20110605032335/http:/www.numdam.org/numdam-bin/fitem%3Fid=AIF_1995__45_4_1037_0%23%7Carchive-date=2011-06-05%7Curl-status=dead%7Cdoi-access=free http://www.math.umn.edu/~garrett/m/buildings https://archive.org/details/geometricveincox0000unse/page/519 https://archive.org/details/lecturesonbuildi0000rona https://www.springer.com/mathematics/numbers/book/978-3-540-22290-3 http://hal.inria.fr/docs/00/09/43/63/PDF/_04a5_Euclidean_buildings_Grenoble_.pdf |
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In der Mathematik sind Bruhat-Tits-Gebäude eine nicht-archimedische Variante symmetrischer Räume. Sie sind nach François Bruhat und Jacques Tits benannt. (de) In mathematics, a building (also Tits building, named after Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces. Buildings were initially introduced by Jacques Tits as a means to understand the structure of exceptional groups of Lie type. The more specialized theory of Bruhat–Tits buildings (named also after François Bruhat) plays a role in the study of p-adic Lie groups analogous to that of the theory of symmetric spaces in the theory of Lie groups. (en) En mathématiques, un immeuble, aussi appelé l’immeuble Tits et l’immeuble Bruhat-Tits (nommé d'après François Bruhat et Jacques Tits) est une structure combinatoire et géométrique qui généralise simultanément certains aspects des variétés de drapeaux, des plans projectifs finis, et les espaces riemanniens symétriques. Introduite par Jacques Tits comme moyen de comprendre la structure des groupes exceptionnels de type de Lie, la théorie a également été utilisée pour l'étude de la géométrie et de la topologie des espaces homogènes des et leurs sous-groupes de symétrie discrets, de la même manière que les arbres ont été utilisés pour étudier les groupes libres. (fr) 数学における（ティッツの、あるいはブリュア–ティッツの）建物（たてもの、英: building, 仏: immeuble）は、とジャック・ティッツに名を因む、旗多様体、有限射影平面およびのある種の側面を一斉に一般化する組合せ論的かつ幾何学的な構造である。初め、建物はジャック・ティッツによっての構造を理解するための手段として導入され、その理論は自由群の研究に木が用いられたのと同じ仕方で、その離散的対称変換部分群の等質空間の幾何および位相を研究するのにも用いられた。 (ja) |
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