Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 2, pp. 389399 (2004) 

Mappings of the sets of invariant subspaces of null systemsMark PankovInstitute of Mathematics NASU, Kiev, email: pankov@imath.kiev.uaAbstract: Let ${\mathcal P}$ and ${\mathcal P}'$ be $(2k+1)$dimensional Pappian projective spaces. Let also $f:{\mathcal P}\to{\mathcal P}^{*}$ and $f':{\mathcal P}'\to {{\mathcal P}'}^*$ be null systems. Denote by ${\mathcal G}_{k}(f)$ and ${\mathcal G}_{k}(f')$ the sets of all invariant $k$dimensional subspaces of $f$ and $f'$, respectively. In the paper we show that if $k\ge 2$ then any mapping of ${\mathcal G}_{k}(f)$ to ${\mathcal G}_{k}(f')$ sending base subsets to base subsets is induced by a strong embedding of ${\mathcal P}$ to ${\mathcal P}'$. Keywords: Grassmann space, null system, base subset Classification (MSC2000): 51M35, 14M15 Full text of the article:
Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.
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