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| Artikel-Nr.: 5667A-9783642078330 Herst.-Nr.: 9783642078330 EAN/GTIN: 9783642078330 |
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![](/p.gif) | 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. Weitere Informationen: ![](/p.gif) | ![](/p.gif) | Author: | Jacques Tits; Richard M. Weiss | Verlag: | Springer Berlin | Sprache: | eng |
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![](/p.gif) | Weitere Suchbegriffe: Buildings, Graph, algebra, classification, combinatorics, generalized polygons, graph theory, incidence geometry, polygon, Buildings; Graph; Algebra; classification; combinatorics; generalizedpolygons; graphtheory; IncidenceGeometry; Polygon |
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