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
( 𝑛 ∑ 𝑖 = 0 𝜆 𝑖 𝐱 𝑖 ) 𝜎 = 𝑛 ∑ 𝑖 = 0 𝜆 𝜎 𝑖 𝐱 𝜎 𝑖 that
-dimensional linear subspaces are mapped to 𝑑 -dimensional linear subspaces and containment/incidence is preserved. Hence 𝑑 induces a collineation. 𝜎
Properties
Consider the projective space
- Automorphic collineätion criterion (fixes basis elements)