Orthogonality and complementation in the lattice of subspaces of a finite vector space

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73612701" target="_blank" >RIV/61989592:15310/22:73612701 - isvavai.cz</a>
Result on the web
<a href="https://mb.math.cas.cz/full/147/2/mb147_2_1.pdf" target="_blank" >https://mb.math.cas.cz/full/147/2/mb147_2_1.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/MB.2021.0042-20" target="_blank" >10.21136/MB.2021.0042-20</a>

Result language
angličtina
Original language name
Orthogonality and complementation in the lattice of subspaces of a finite vector space
Original language description
We investigate the lattice L(V) of subspaces of an n-dimensional vector space V over a finite field GF(q) where q is a prime power of a prime p together with the unary operation of orthogonality. It is known that this lattice is modular and that the orthogonality is an antitone involution. The lattice L(V) satisfies the chain condition and we determine the number of covers of its elements, especially the number of atoms. We characterize when orthogonality is a complementation and hence when L(V) is orthomodular. If q is a prime number and the dimension is equal to 2, we characterize orthomodularity of L(V) by a simple condition.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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