On bijections that preserve complementarity of subspaces

Andrea Blunck; Hans Havlicek

doi:10.1016/j.disc.2004.11.018

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arXiv · 1304.0180

On bijections that preserve complementarity of subspaces

Andrea Blunck·Hans Havlicek

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Abstract

The set $G$ of all $m$-dimensional subspaces of a $2m$-dimensional vector space $V$ is endowed with two relations, complementarity and adjacency. We consider bijections from $G$ onto $G'$, where $G'$ arises from a $2m'$-dimensional vector space $V'$. If such a bijection $\phi$ and its inverse leave one of the relations from above invariant, then also the other. In case $m\geq 2$ this yields that $\phi$ is induced by a semilinear bijection from $V$ or from the dual space of $V$ onto $V'$. As far as possible, we include also the infinite-dimensional case into our considerations.

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Andrea Blunck, Hans Havlicek. 2013-03-31. On bijections that preserve complementarity of subspaces. https://doi.org/10.1016/j.disc.2004.11.018

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