On bijections that preserve complementarity of subspaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2013
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| _version_ | 1866911774267146240 |
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| author | Blunck, Andrea Havlicek, Hans |
| author_facet | Blunck, Andrea Havlicek, Hans |
| contents | 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 $ϕ$ and its inverse leave one of the relations from above invariant, then also the other. In case $m\geq 2$ this yields that $ϕ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1304_0180 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | On bijections that preserve complementarity of subspaces Blunck, Andrea Havlicek, Hans Algebraic Geometry Combinatorics 51A10, 51A45, 05C60 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 $ϕ$ and its inverse leave one of the relations from above invariant, then also the other. In case $m\geq 2$ this yields that $ϕ$ 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. |
| title | On bijections that preserve complementarity of subspaces |
| topic | Algebraic Geometry Combinatorics 51A10, 51A45, 05C60 |
| url | https://arxiv.org/abs/1304.0180 |