On Automorphisms of Flag Spaces

Abstract

We show that the automorphisms of the flag space associated with a 3-dimensional projective space can be characterized as bijections preserving a certain binary relation on the set of flags in both directions. From this we derive that there are no other automorphisms of the flag space than those coming from collineations and dualities of the underlying projective space. Further, for a commutative ground field, we discuss the corresponding flag variety and characterize its group of automorphic collineations. Mathematics Subject Classification (2000): 51M35, 51N15, 15A75, 14M15.

Die Linienelemente des 𝕡³

“…Die Geometrie der verallgemeinerten Raumelemente sowie ihr Zusammenhang mit der Darstellungstheorie der endlichen Gruppen war bereits Gegenstand zahlreicher Untersuchungen, siehe hierzu etwa [1][2][3][4]7].…”