In 1982 Bichara and Mazzocca characterized the Grassmann space $Gr(1,\AA)$ of the lines of an affine space $\AA$ of dimension at least 3 over a skew--field $K$ by means of the intersection properties of the three disjoint families $\Sigma_1, \Sigma_2$ and $\cal T$ of maximal singular subspaces of $Gr(1,\AA)$. In this paper we deal with the characterization of $Gr(1,\AA)$ using only the family $\Sigma=\Sigma_1 \cup \Sigma_2$ of maximal singular subspaces.
On the Grassmann space representing the lines of an affine space
FERRARA DENTICE, Eva;
2012
Abstract
In 1982 Bichara and Mazzocca characterized the Grassmann space $Gr(1,\AA)$ of the lines of an affine space $\AA$ of dimension at least 3 over a skew--field $K$ by means of the intersection properties of the three disjoint families $\Sigma_1, \Sigma_2$ and $\cal T$ of maximal singular subspaces of $Gr(1,\AA)$. In this paper we deal with the characterization of $Gr(1,\AA)$ using only the family $\Sigma=\Sigma_1 \cup \Sigma_2$ of maximal singular subspaces.File in questo prodotto:
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