Geometry of block triangular matrices over a division ring

Let D be a division ring with and T(ni,k) denote the set of k × k block triangular matrices over D. Let be a bijective map from to itself such that both and −1 preserve the adjacency. By the method of maximal sets of rank one and affine geometry, we characterize and obtain the fundamental theorem of the geometry on T(ni,k). As a corollary, weakly block-additive adjacency preserving bijective maps in both directions on T(ni,k) are characterized. As applications of the fundamental theorem, ring automorphisms or ring anti-automorphisms of T(ni,k) are characterized, and Jordan automorphisms of Jordan ring J(T(ni,k)) are also characterized.