Boolean subalgebras of orthoalgebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F19%3A00335506" target="_blank" >RIV/68407700:21230/19:00335506 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11083-019-09483-6" target="_blank" >https://doi.org/10.1007/s11083-019-09483-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11083-019-09483-6" target="_blank" >10.1007/s11083-019-09483-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Boolean subalgebras of orthoalgebras

Popis výsledku v původním jazyce

We develop a direct method to recover an orthoalgebra from its poset of Boolean subalgebras. For this a new notion of direction is introduced. Directions are also used to characterize in purely order-theoretic terms those posets that are isomorphic to the poset of Boolean subalgebras of an orthoalgebra. These posets are characterized by simple conditions defining orthodomains and the additional requirement of having enough directions. Excepting pathologies involving maximal Boolean subalgebras of four elements, it is shown that there is an equivalence between the category of orthoalgebras and the category of orthodomains with enough directions with morphisms suitably defined. Furthermore, we develop a representation of orthodomains with enough directions, and hence of orthoalgebras, as certain hypergraphs. This hypergraph approach extends the technique of Greechie diagrams and resembles projective geometry. Using such hypergraphs, every orthomodular poset can be represented by a set of points and lines where each line contains exactly three points.

Název v anglickém jazyce

Boolean subalgebras of orthoalgebras

Popis výsledku anglicky

We develop a direct method to recover an orthoalgebra from its poset of Boolean subalgebras. For this a new notion of direction is introduced. Directions are also used to characterize in purely order-theoretic terms those posets that are isomorphic to the poset of Boolean subalgebras of an orthoalgebra. These posets are characterized by simple conditions defining orthodomains and the additional requirement of having enough directions. Excepting pathologies involving maximal Boolean subalgebras of four elements, it is shown that there is an equivalence between the category of orthoalgebras and the category of orthodomains with enough directions with morphisms suitably defined. Furthermore, we develop a representation of orthodomains with enough directions, and hence of orthoalgebras, as certain hypergraphs. This hypergraph approach extends the technique of Greechie diagrams and resembles projective geometry. Using such hypergraphs, every orthomodular poset can be represented by a set of points and lines where each line contains exactly three points.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS

ISSN

0167-8094

e-ISSN

1572-9273

Svazek periodika

36

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

47

Strana od-do

563-609

Kód UT WoS článku

000509936700010

EID výsledku v databázi Scopus

2-s2.0-85062777699