Abstract projective space

Collineätion

A collineätion is an isomorphism of (abstract) projective spaces , geo i.e. a bijection which preserves the incidence of subspaces. The set of all collineations is a group, which for a projectivization is the Projective semilinear group.

Types of collineation

By the Fundamental theorem of projective geometry, the only collineations of a projectivization are

• Projective semilinear group
  • Homography given by a linear transformation of the underlying vector space (Projective general linear group)
  • Automorphic collineätion given by a coördinatewise Field automorphism

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