Linear Orthosets and Orthogeometries

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134224" target="_blank" >RIV/00216224:14310/23:00134224 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10773-023-05282-3" target="_blank" >https://doi.org/10.1007/s10773-023-05282-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-023-05282-3" target="_blank" >10.1007/s10773-023-05282-3</a>

Result language
angličtina
Original language name
Linear Orthosets and Orthogeometries
Original language description
Anisotropic Hermitian spaces can be characterised as anisotropic orthogeometries, that is, as projective spaces that are additionally endowed with a suitable orthogonality relation. But linear dependence is uniquely determined by the orthogonality relation and hence it makes sense to investigate solely the latter. It turns out that by means of orthosets, which are structures based on a symmetric, irreflexive binary relation, we can achieve a quite compact description of the inner-product spaces under consideration. In particular, Pasch's axiom, or any of its variants, is no longer needed. Having established the correspondence between anisotropic Hermitian spaces on the one hand and so-called linear orthosets on the other hand, we moreover consider the respective symmetries. We present a version of Wigner's Theorem adapted to the present context.
Czech name
—
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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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