Point-Line Characterizations of Buildings

摘要

Lie incidence system and Lie incidence structure are discussed. The construction method of shadow spaces of type B (a building of type M over an index I) over i (i element of I), is given. The analog of the coordinatization theorem for (other) buildings and the classification of geometries with spherical Coxeter diagram, are used. Veblen-Young theorem is proved. A shadow space determined by a building is characterized by the full shadow space (a particular projective space). Characterization theorems are proved. Tits geometry can be identified as a building. Axiomatic theory of shadow spaces is reported.