Characterizing symplectic quadrangles by their derivations
The author shows that a generalized quadrangle \({\mathcal Q}\) is isomorphic to the geometry of absolute points and lines with respect to a symplectic polarity of a 3-dimensional projective space if and only if the derivation at every point of \({\mathcal Q}\) yields a projective plane. The proof is achieved as a nice application of the axiom system of Winternitz. Furthermore, the author examines the case of locally compact connected quadrangles more closely and gives several characterizations of the symplectic quadrangles over the fields \(\mathbb{R}\) and \(\mathbb{C}\).
scientific article; zbMATH DE number 62258
scientific article