Categories of orthogonality spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F22%3A00119310" target="_blank" >RIV/00216224:14310/22:00119310 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jpaa.2021.106859" target="_blank" >https://doi.org/10.1016/j.jpaa.2021.106859</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2021.106859" target="_blank" >10.1016/j.jpaa.2021.106859</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Categories of orthogonality spaces

Popis výsledku v původním jazyce

An orthogonality space is a set equipped with a symmetric and irreflexive binary relation. We consider orthogonality spaces with the additional property that any collection of mutually orthogonal elements gives rise to the structure of a Boolean algebra. Together with the maps that preserve the Boolean substructures, we are led to the category NOS of normal orthogonality spaces. Moreover, an orthogonality space of finite rank is called linear if for any two distinct elements e and f there is a third one g such that exactly one of f and g is orthogonal to e and the pairs e, f and e, g have the same orthogonal complement. Linear orthogonality spaces arise from finite-dimensional Hermitian spaces. We are led to the full subcategory LOS of NOS and we show that the morphisms are the orthogonality-preserving lineations. Finally, we consider the full subcategory OS pound of LOS whose members arise from positive definite Hermitian spaces over Baer ordered *-fields with a Euclidean fixed field. We establish that the morphisms of OS pound are induced by generalised semiunitary mappings.

Název v anglickém jazyce

Categories of orthogonality spaces

Popis výsledku anglicky

An orthogonality space is a set equipped with a symmetric and irreflexive binary relation. We consider orthogonality spaces with the additional property that any collection of mutually orthogonal elements gives rise to the structure of a Boolean algebra. Together with the maps that preserve the Boolean substructures, we are led to the category NOS of normal orthogonality spaces. Moreover, an orthogonality space of finite rank is called linear if for any two distinct elements e and f there is a third one g such that exactly one of f and g is orthogonal to e and the pairs e, f and e, g have the same orthogonal complement. Linear orthogonality spaces arise from finite-dimensional Hermitian spaces. We are led to the full subcategory LOS of NOS and we show that the morphisms are the orthogonality-preserving lineations. Finally, we consider the full subcategory OS pound of LOS whose members arise from positive definite Hermitian spaces over Baer ordered *-fields with a Euclidean fixed field. We establish that the morphisms of OS pound are induced by generalised semiunitary mappings.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF20-09869L" target="_blank" >GF20-09869L: Ortomodularita z různých pohledů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

1873-1376

Svazek periodika

226

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

22

Strana od-do

106859

Kód UT WoS článku

000704010100011

EID výsledku v databázi Scopus

2-s2.0-85111757693