Embeddings of affine Grassmann spaces
The authors prove that if a Grassmann space \( \Delta =Gr_{{\mathbb{A}}}(m, h, K)\) of the \(h\)-subspaces of an affine space \(\mathbb{A}= AG(m,K)\) has an embedding \(e\) into a projective space \(PG(n,K^\prime)\) over a skew-field \(K^\prime\), and \(e\) satisfies two suitable conditions \((\alpha )\) and \((\beta )\), then \(K\) and \(K^\prime\) are isomorphic fields and \(\Delta^{e}\) is, up to projections, an affine Grassmannian.
scientific article; zbMATH DE number 5637116