Automorphic collineation
An automorphic collineätion is a Collineätion of a projective space given by a field automorphism applied coördinatewise, geo
hence it is the action of
Proof of collineation
It follows from
that
-dimensional linear subspaces are mapped to -dimensional linear subspaces and containment/incidence is preserved. Hence induces a collineation.
Properties
Consider the projective space
- Automorphic collineätion criterion (fixes basis elements)