A Jacobson Radical Decomposition of the Fano-Snowflake Configuration

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dc.creatorSaniga, Metod
dc.creatorPracna, Petr
dc.date2008-07-11
dc.date2008-10-27
dc.date.accessioned2026-07-07T10:12:55Z
dc.date.available2026-07-07T10:12:55Z
dc.descriptionThe Fano-Snowflake, a specific $non$-unimodular projective lattice configuration associated with the smallest ring of ternions $R_{\diamondsuit}$ (arXiv:0803.4436 and 0806.3153), admits an interesting partitioning with respect to the Jacobson radical of $R_{\diamondsuit}$. The totality of 21 free cyclic submodules generated by non-unimodular vectors of the free left $R_{\diamondsuit}$-module $R_{\diamondsuit}^{3}$ are shown to split into three disjoint sets of cardinalities 9, 9 and 3 according as the number of Jacobson radical entries in the generating vector is 2, 1 or 0, respectively. The corresponding "ternion-induced" factorization of the lines of the Fano plane sitting in the middle of the Fano-Snowflake (6 -- 7 -- 3) is found to $differ fundamentally$ from the natural one, i. e., from that with respect to the Jacobson radical of the Galois field of two elements (3 -- 3 -- 1).
dc.description7 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0807.1790
dc.identifierhttp://arxiv.org/abs/0807.1790
dc.identifierSIGMA 4 (2008) 072, 7 pages
dc.identifierdoi:10.3842/SIGMA.2008.072
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172351
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.subjectQuantum Physics
dc.titleA Jacobson Radical Decomposition of the Fano-Snowflake Configuration
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