Abstract :
Noncommutativity of the ground field has a deep influence on the geometry of projective spaces, as shown, for instance, by the failure of Pappus’ theorem. In this paper we observe that in noncommutative geometry the system of fixed points of a collineation is a particular union of projective subgeometries coordinatized by suitable division subrings. Since the study of fixed points of a collineation leads to consider eigenvalues and eigenvectors of semilinear transformations, we present the theory, which is interesting in itself, of eigenvalues and eigenvectors of semilinear transformations over division rings.
