From Cayley-Dickson Algebras to Combinatorial Grassmannians

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

From Cayley-Dickson Algebras to Combinatorial Grassmannians

Original language description

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

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

CF - Physical chemistry and theoretical chemistry

OECD FORD branch

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Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2015

Confidentiality

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

Name of the periodical

Mathematics

ISSN

2227-7390

e-ISSN

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Volume of the periodical

3

Issue of the periodical within the volume

4

Country of publishing house

CH - SWITZERLAND

Number of pages

30

Pages from-to

1192-1221

UT code for WoS article

000367619000012

EID of the result in the Scopus database

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