Geometry of the hypercomplexes of lines in a multidimensional affine space. II (Q1382870)

[For Part I, see Zbl 0804.53016.] In the affine \(n\)-dimensional space the hypercomplex \(Gr(l,n, 2n-3)\) is studied. To every line \(\ell\) of \(Gr(l,n, 2n-3)\) the three-dimensional normal \(N_3(\ell)\) and the \((n-4)\)-dimensional normal \(N_{n-4} (\ell)\) are defined. A certain correspondence between the normal spaces is found. To every point of \(N_3(\ell)\) there corresponds an \((n-5)\)-plane of \(N_{n-4} (\ell)\) \((n\geq 5)\); to each point of \(N_{n-4} (\ell)\) there corresponds a two-dimensional plane of \(N_3(\ell)\). If such correspondence is undefined, then some invariant correspondence between normal spaces exists. With the help of the space \(N_{n-4} (\ell)\) a certain bundle of hyperplanes is found. The axis of this bundle is the three-dimensional space \(N_3 (\ell)\). Hence it determines the second correspondences between normal spaces. If both introduced correspondences between normal spaces are satisfied, then an invariant inner equipment (normalization) of the lines of \(Gr (l,n,2n-3)\) can be found.