Twin ''Fano-Snowflakes'' over the Smallest Ring of Ternions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Twin ''Fano-Snowflakes'' over the Smallest Ring of Ternions
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| Creator |
Saniga, M.
Havlicek, H. Planat, M. Pracna, P. |
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| Description |
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.
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| Date |
2019-02-19T13:10:07Z
2019-02-19T13:10:07Z 2008 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2000 Mathematics Subject Classification: 51C05; 51Exx http://dspace.nbuv.gov.ua/handle/123456789/149031 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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