Twin "Fano-Snowflakes" Over the Smallest Ring of Ternions
1.
SYSNO ASEP
0310815
Druh ASEP
J - Článek v odborném periodiku
Zařazení RIV
J - Článek v odborném periodiku
Poddruh J
Ostatní články
Název
Twin "Fano-Snowflakes" Over the Smallest Ring of Ternions
Překlad názvu
Dvojčata "Fano sněhových vloček" nad nejmenším okruhem ternionů
Tvůrce(i)
Saniga, M. (SK) Havlicek, H. (AT) Planat, M. (FR) Pracna, Petr (UFCH-W)
Zdroj.dok.
Symmetry, Integrability and Geometry: Methods and Applications. - : Natsional'na Akademiya Nauk Ukrainy
- ISSN 1815-0659
Roč. 4, - (2008), 050-1-7
Poč.str.
7 s.
Jazyk dok.
eng - angličtina
Země vyd.
UA - Ukrajina
Klíč. slova
geometry over rings ; non-communicative ring of order eight ; Fano plane
Vědní obor RIV
CF - Fyzikální chemie a teoretická chemie
CEZ
AV0Z40400503 - UFCH-W (2005-2011)
Anotace
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.
