{"product_id":"moufang-polygons-von-jacques-tits-richard-m-weiss","title":"Moufang Polygons","description":"Spherical buildings are certain combinatorial simplicial complexes intro duced, at first in the language of \"incidence geometries,\" to provide a sys tematic geometric interpretation of the exceptional complex Lie groups. (The definition of a building in terms of chamber systems and definitions of the various related notions used in this introduction such as \"thick,\" \"residue,\" \"rank,\" \"spherical,\" etc. are given in Chapter 39. ) Via the notion of a BN-pair, the theory turned out to apply to simple algebraic groups over an arbitrary field. More precisely, to any absolutely simple algebraic group of positive rela tive rank £ is associated a thick irreducible spherical building of the same rank (these are the algebraic spherical buildings) and the main result of Buildings of Spherical Type and Finite BN-Pairs [101] is that the converse, for £ ::::: 3, is almost true: (1. 1) Theorem. Every thick irreducible spherical building of rank at least three is classical, algebraic' or mixed. Classical buildings are those defined in terms of the geometry of a classical group (e. g. unitary, orthogonal, etc. of finite Witt index or linear of finite dimension) over an arbitrary field or skew-field. (These are not algebraic if, for instance, the skew-field is of infinite dimension over its center. ) Mixed buildings are more exotic; they are related to groups which are in some sense algebraic groups defined over a pair of fields k and K of characteristic p, where KP eke K and p is two or (in one case) three.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642078330\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783540437147\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642078330","offer_id":39437534462045,"sku":"9783642078330","price":106.99,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783540437147","offer_id":51569213382,"sku":"9783540437147","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/43b1d230-53f5-4167-988d-a169509d2f48.jpg?v=1774589224","url":"https:\/\/shop.autorenwelt.de\/products\/moufang-polygons-von-jacques-tits-richard-m-weiss","provider":"Autorenwelt Shop","version":"1.0","type":"link"}