Dvojčata "Fano sněhových vloček" nad nejmenším okruhem ternionů

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61388955%3A_____%2F08%3A00310815" target="_blank" >RIV/61388955:_____/08:00310815 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Twin "Fano-Snowflakes" Over the Smallest Ring of Ternions

Popis výsledku v původním jazyce

Given a finite associative ring with unity, R, any free (left) cyclic submodule (FCS) generated by a unimodular (n + 1)-tuple of elements of R represents a point of the n-dimensional projective space over R. Suppose that R also features FCSs generated by(n + 1)-tuples that are not unimodular: what kind of geometry can be ascribed to such FCSs? Here, we (partially) answer this question for n = 2 when R is the (unique) non-commutative ring of order eight. The corresponding geometry is dubbed a "Fano-Snowflake" due to its diagrammatic appearance and the fact that it contains the Fano plane in its center. There exist, in fact, two such configurations - each being tied to either of the two maximal ideals of the ring - which have the Fano plane in common and can, therefore, be viewed as twins. Potential physical relevance of these noteworthy configurations for quantum information theory and stringy black holes is also outlined.

Název v anglickém jazyce

Twin "Fano-Snowflakes" Over the Smallest Ring of Ternions

Popis výsledku anglicky

Given a finite associative ring with unity, R, any free (left) cyclic submodule (FCS) generated by a unimodular (n + 1)-tuple of elements of R represents a point of the n-dimensional projective space over R. Suppose that R also features FCSs generated by(n + 1)-tuples that are not unimodular: what kind of geometry can be ascribed to such FCSs? Here, we (partially) answer this question for n = 2 when R is the (unique) non-commutative ring of order eight. The corresponding geometry is dubbed a "Fano-Snowflake" due to its diagrammatic appearance and the fact that it contains the Fano plane in its center. There exist, in fact, two such configurations - each being tied to either of the two maximal ideals of the ring - which have the Fano plane in common and can, therefore, be viewed as twins. Potential physical relevance of these noteworthy configurations for quantum information theory and stringy black holes is also outlined.

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

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2008

Kód důvěrnosti údajů

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

Název periodika

Symmetry, Integrability and Geometry: Methods and Applications

ISSN

1815-0659

e-ISSN

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Svazek periodika

4

Číslo periodika v rámci svazku

-

Stát vydavatele periodika

UA - Ukrajina

Počet stran výsledku

7

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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