ISBN: 9783540437147

Spherical buildings are certain combinatorial simplicial complexes intro­ duced, at first in the language of ""incidence geometries,"" to provide a sys­ tematic geometric interpretation… Mehr…

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. | Moufang Polygons by Jacques Tits Hardcover | Indigo Chapters Books > Science & Nature > Math & Physics > Mathematics P10117, Jacques Tits<

2002, ISBN: 9783540437147

Buch, Hardcover, 2002, This book gives the complete classification of Moufang polygons, starting from first principles. In particular, it may serve as an introduction to the various impor… Mehr…

Buch, Hardcover, 2002, This book gives the complete classification of Moufang polygons, starting from first principles. In particular, it may serve as an introduction to the various important algebraic concepts which arise in this classification including alternative division rings, quadratic Jordan division algebras of degree three, pseudo-quadratic forms, BN-pairs and norm splittings of quadratic forms. This book also contains a new proof of the classification of irreducible spherical buildings of rank at least three based on the observation that all the irreducible rank two residues of such a building are Moufang polygons. In an appendix, the connection between spherical buildings and algebraic groups is recalled. [PU: Springer Berlin], Seiten: 535, Springer Berlin, 2002<

2002, ISBN: 3540437142

[EAN: 9783540437147], Neubuch, [PU: Springer Berlin Heidelberg], GEOMETRIE RAUMLEHRE BUILDINGS GRAPH ALGEBRA CLASSIFICATION COMBINATORICS GENERALIZEDPOLYGONS GRAPHTHEORY INCIDENCEGEOMETRY… Mehr…

[EAN: 9783540437147], Neubuch, [PU: Springer Berlin Heidelberg], GEOMETRIE RAUMLEHRE BUILDINGS GRAPH ALGEBRA CLASSIFICATION COMBINATORICS GENERALIZEDPOLYGONS GRAPHTHEORY INCIDENCEGEOMETRY POLYGON MATHEMATIK GENERALIZED POLYGONS THEORY INCIDENCE GEOMETRY DISCRETE MATHEMATICS ALGEBRAIC GEOM, Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Gives a complete classification of Moufang polygons, starting from first principlesIncludes a totally new classification of the spherical buildings of rank 3 at, Books<

2002, ISBN: 3540437142

[EAN: 9783540437147], Neubuch, [PU: Springer 2002-09-12], Books

2002, ISBN: 9783540437147

Buch, Hardcover, 2002, [PU: Springer Berlin], Springer Berlin, 2002