We consider the standard quantum logic ${\mathcal L}(H)$ associated to a complex Hilbert space $H$, i.e. the lattice of closed subspaces of $H$ together with the orthogonal complementation. The… Expand

We describe all possible isomorphisms between connected components of Grassmann graphs associated to vector spaces $$X$$X and $$Y$$Y, respectively. As an application, we characterize compementarity… Expand

Part 1 Linear algebra over division rings: matrices over division rings matrix representations of subspaces systems of linear equations. Part 2 Affine geometry and projective geometry: affine spaces… Expand

These notes are a slightly revised and extended version of mim- graphed notes written on the occasion of a seminar on buildings and BN-pairs held at Oberwolfach in April 1968. Their main purpose is… Expand