Moufang Polygons (e-bog) af Weiss, Richard M.
Weiss, Richard M. (forfatter)

Moufang Polygons e-bog

875,33 DKK (inkl. moms 1094,16 DKK)
Spherical buildings are certain combinatorial simplicial complexes intro- duced, at first in the language of &quote;incidence geometries,&quote; 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 &quote;thick,&quote; &q...
E-bog 875,33 DKK
Forfattere Weiss, Richard M. (forfatter)
Forlag Springer
Udgivet 9 marts 2013
Genrer PBD
Sprog English
Format pdf
Beskyttelse LCP
ISBN 9783662046890
Spherical buildings are certain combinatorial simplicial complexes intro- duced, at first in the language of "e;incidence geometries,"e; 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 "e;thick,"e; "e;residue,"e; "e;rank,"e; "e;spherical,"e; 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 GBP 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 GBP ::::: 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.