Graphs, defined by Weyl distance or incidence, that determine a vector space. (English) Zbl 1302.15002
Summary: We study to which extent the family of pairs of subspaces of a vector space related to each other via intersection properties determines the vector space. In another language, we study to which extent the family of vertices of the building of a projective space related to each other via several natural respective conditions involving the Weyl distance and incidence determines the building. These results can be seen as generalizations of and variations on the Fundamental Theorem of Projective Geometry.
MSC:
| 15A03 | Vector spaces, linear dependence, rank, lineability |
| 15A04 | Linear transformations, semilinear transformations |
| 51A05 | General theory of linear incidence geometry and projective geometries |
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