{"product_id":"9783540437147","title":"Springer Monographs in Mathematics","description":"\u003ch1\u003eSpringer Monographs in Mathematics\u003c\/h1\u003e \u003ch2\u003eTits, Jacques; Weiss, Richard M.\u003c\/h2\u003e \u003cp\u003eSpherical 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2002-09-12\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540437147\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-662-04689-0\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 535\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":44521573417100,"sku":"9783540437147","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540437147.jpg?v=1775705796","url":"https:\/\/lateknightbooks.com\/products\/9783540437147","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}