Fano-Snowflake构型的Jacobson根分解

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摘要翻译：
Fano-Snowflake是一种特殊的$非$单模射影晶格构型，它与最小的ternions环$R_{\diamondsuit}$(arxiv:0803.4436和0806.3153)相关联，它对$R_{\diamondsuit}$的Jacobson根有一个有趣的划分。由自由左$R_{\diamondsuit}$-模$R_{\diamondsuit}^{3}$的非单模向量生成的21个自由循环子模的整体，根据生成向量中Jacobson根项的个数分别为2,1或0,分裂为基数9,9和3的三个不相交集。在Fano-Snowflake(6--7--3)中间的Fano平面线的相应的“三元诱导”因式分解与自然的因式分解有根本的不同。E.从关于两元Galois场的Jacobson根（3-3-1）。
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英文标题：
《A Jacobson Radical Decomposition of the Fano-Snowflake Configuration》
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作者：
Metod Saniga (ASTRINSTSAV), Petr Pracna (JH-Inst)
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--
一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
--
一级分类：Physics        物理学
二级分类：Quantum Physics        量子物理学
分类描述：Description coming soon
描述即将到来
--

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英文摘要：
  The 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).
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PDF链接：
https://arxiv.org/pdf/0807.1790

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关键词：Jacobs Jacob Flak Snow Lake 诱导 相应 生成 平面 因式分解