105 research outputs found
Embeddings of Grassmann graphs
Let and be vector spaces of dimension and , respectively.
Let and . We describe all isometric
and -rigid isometric embeddings of the Grassmann graph in
the Grassmann graph
Geometrical characterization of semilinear isomorphisms of vector spaces and semilinear homeomorphisms of normed spaces
Let and be vector spaces over division rings (possible
infinite-dimensional) and let and be the
associated projective spaces. We say that is a PGL-{\it mapping} if for every there exists
such that . We show that for every PGL-bijection
the inverse mapping is a semicollineation. Also, we obtain an analogue of this
result for the projective spaces associated to normed spaces
Base subsets of polar Grassmannians
Let be a thick building of type
. Let also be
the Grassmannian of -dimensional singular subspaces of the associated polar
space (of rank ). We write for the corresponding
shadow space of type . Every bijective transformation of
sending base subsets to base subsets (the shadows of
apartments) is a collineation of , and it is induced by a
collineation of if or
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