Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 389-399 (2004)

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Mappings of the sets of invariant subspaces of null systems

Mark Pankov

Institute of Mathematics NASU, Kiev, e-mail:

Abstract: 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

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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.

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