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A Jacobson Radical Decomposition of the Fano-Snowflake Configuration
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4
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- Symmetry, Integrability and Geometry: Methods and Applications, 2008, том 4, випуск за цей рік
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A Jacobson Radical Decomposition of the Fano-Snowflake Configuration
Інший ID:
2000 Mathematics Subject Classification: 51C05; 51Exx
Посилання:
A Jacobson Radical Decomposition of the Fano-Snowflake Configuration / M. Saniga, P. Pracna // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 8 назв. — англ.
Підтримка:
The work was partially supported by the VEGA grant agency projects Nos. 6070 and 7012, the CNRS-SAV Project No. 20246 and by the Action Austria–Slovakia project No. 58s2. We thank Hans Havlicek (Vienna University of Technology) for valuable comments and suggestions.
Дата:
2008
Переглядів:
617
Завантажень:
252
Анотація:
The Fano-Snowflake, a specific configuration associated with the smallest ring of ternions Rà (arXiv:0803.4436 and arXiv:0806.3153), admits an interesting partitioning with respect to the Jacobson radical of Rà. The totality of 21 free cyclic submodules generated by non-unimodular vectors of the free left Rà-module Rà³ is 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 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.
