Isomorphisms of Affine Pl\"ucker Spaces

TL;DR

This paper proves that all isomorphisms of Plücker spaces on affine spaces of dimension three or higher are induced by collineations of the original affine spaces, establishing a fundamental geometric correspondence.

Contribution

It demonstrates that every isomorphism of affine Plücker spaces is derived from a collineation, clarifying the structure of these geometric transformations.

Findings

All isomorphisms of Plücker spaces are from collineations.

The result holds for affine spaces with dimension at least 3.

Provides a complete characterization of these isomorphisms.

Abstract

All isomorphisms of Pl\"ucker spaces on affine spaces with dimensions $\geq 3$ arise from collineations of the underlying affine spaces.