TY - BOOK
AU - Shult,Ernest E.
TI - Points and lines: characterizing the classical geometries
T2 - Universitext
SN - 9783642156267
U1 - 516.02 23
PY - 2011///
CY - Berlin
PB - Springer
KW - GeometrÃa
KW - Geometry
KW - MatemÃ¡ticas
KW - Mathematics
N1 - Includes bibliographical references and index; Basics About Graphs -- Geometries: Basic Concepts -- Point-Line Geometries -- Hyperplanes, Embeddings, and Teirlinckâs Theory -- Projective Planes -- Projective Spaces -- Polar Spaces -- Near Polygons -- Chamber Systems and Buildings - 2-Covers of Chamber Systems -- Locally Truncated Diagram Geometries -- Separated Systems of Singular Spaces -- Coopersteinâs Theory of Symplecta and Parapolar Spaces -- Characterizations of the Classical Grassmann Spaces -- Characterizing the Classical Strong Parapolar Spaces: The CohenâCooperstein Theory Revisited -- Characterizing Strong Parapolar Spaces by the Relation Between Points and Certain Maximal Singular Subspaces -- Point-Line Characterizations of the âLong Root Geometriesâ -- The Peculiar Pentagon Property
N2 - The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups
ER -