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dc.contributor.author Saniga, M.
dc.contributor.author Havlicek, H.
dc.contributor.author Planat, M.
dc.contributor.author Pracna, P.
dc.date.accessioned 2019-02-19T13:10:07Z
dc.date.available 2019-02-19T13:10:07Z
dc.date.issued 2008
dc.identifier.citation Twin ''Fano-Snowflakes'' over the Smallest Ring of Ternions / M. Saniga, H. Havlicek, M. Planat, P. Pracna // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 25 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2000 Mathematics Subject Classification: 51C05; 51Exx
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/149031
dc.description.abstract 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 relevance of these noteworthy configurations to quantum information theory and stringy black holes is also outlined. uk_UA
dc.description.sponsorship The work was supported by the VEGA grant agency projects Nos. 6070 and 7012, the CNRSSAV Project No. 20246 “Projective and Related Geometries for Quantum Information” and by the Action Austria-Slovakia project No. 58s2 “Finite Geometries Behind Hilbert Spaces”. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Twin ''Fano-Snowflakes'' over the Smallest Ring of Ternions uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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