From Cayley-Dickson Algebras to Combinatorial Grassmannians

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388955%3A_____%2F15%3A00453602" target="_blank" >RIV/61388955:_____/15:00453602 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.3390/math3041192" target="_blank" >http://dx.doi.org/10.3390/math3041192</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math3041192" target="_blank" >10.3390/math3041192</a>

Jazyk výsledku

angličtina

Název v původním jazyce

From Cayley-Dickson Algebras to Combinatorial Grassmannians

Popis výsledku v původním jazyce

Given a 2N -dimensional Cayley-Dickson algebra, where 3 N 6 , we first observe that the multiplication table of its imaginary units ea , 1 a 2N - 1 , is encoded in the properties of the projective space PG(N - 1,2) if these imaginary units are regarded as points and distinguished triads of them {ea, eb , ec} , 1 a < b < c 2N - 1 and eaeb = ec , as lines. This projective space is seen to feature two distinct kinds of lines according as a + b = c or a + b non = c . Consequently, it also exhibits (at leasttwo) different types of points in dependence on how many lines of either kind pass through each of them. In order to account for such partition of the PG(N - 1,2) , the concept of Veldkamp space of a finite point-line incidence structure is employed. The corresponding point-line incidence structure is found to be a specific binomial configuration CN; in particular, C3 (octonions) is isomorphic to the Pasch (62, 43) -configuration, C4 (sedenions) is the famous Desargues (103) -configurat

Název v anglickém jazyce

From Cayley-Dickson Algebras to Combinatorial Grassmannians

Popis výsledku anglicky

Given a 2N -dimensional Cayley-Dickson algebra, where 3 N 6 , we first observe that the multiplication table of its imaginary units ea , 1 a 2N - 1 , is encoded in the properties of the projective space PG(N - 1,2) if these imaginary units are regarded as points and distinguished triads of them {ea, eb , ec} , 1 a < b < c 2N - 1 and eaeb = ec , as lines. This projective space is seen to feature two distinct kinds of lines according as a + b = c or a + b non = c . Consequently, it also exhibits (at leasttwo) different types of points in dependence on how many lines of either kind pass through each of them. In order to account for such partition of the PG(N - 1,2) , the concept of Veldkamp space of a finite point-line incidence structure is employed. The corresponding point-line incidence structure is found to be a specific binomial configuration CN; in particular, C3 (octonions) is isomorphic to the Pasch (62, 43) -configuration, C4 (sedenions) is the famous Desargues (103) -configurat

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

CF - Fyzikální chemie a teoretická chemie

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

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Svazek periodika

3

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

30

Strana od-do

1192-1221

Kód UT WoS článku

000367619000012

EID výsledku v databázi Scopus

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