Search

The Fundamental Theorem of Projective Geometry states that, in a vector space, a permutation of vector lines preserving triples that span a vector plane is induced by a semi-linear automorphism. We consider a generalisation to triples of subspaces, not necessarily of the same dimension, spanning, or being contained in a subspace of fixed dimension. We determine all cases in which the permutation is necessarily induced by a semi-linear automorphism. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]