Minimal fields of definition for simplicial arrangements in the real projective plane
Minimal fields of definition for simplicial arrangements in the real projective plane
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实射影平面上单纯排列的最小定义域
DOI：
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发表时间：
2011
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通讯作者：
M. Cuntz
中科院分区：
文献类型：
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作者：
M. Cuntz
最近我。Heckenberger和作者对秩为3的有限Weyl群胚进行了分类[3]。Weyl广群是Weyl群的推广，参见[2]的介绍。是B。Mühlherr谁注意到，根系统的秩三Weyl广群产生单纯安排在真实的投影平面。感谢B的目录。Grünbaum [4]，很容易识别它们：事实证明，在他的Hasse图的大部分中，67个零星排列中有53个来自Weyl群胚。这是动机足以调查单纯安排从这个新的观点，特别是因为它仍然是一个悬而未决的问题是否目录格伦鲍姆是完整的。
Recently I. Heckenberger and the author have classified the so-called finite Weyl groupoids of rank three [3]. A Weyl groupoid is a generalization of the Weyl group, see [2] for an introduction. It was B. Mühlherr who noticed that the root systems of rank three Weyl groupoids yield simplicial arrangements in the real projective plane. Thanks to the catalogue of B. Grünbaum [4], it was easy to identify them: It turned out that 53 of the 67 sporadic arrangements in the large component of his Hasse diagram come from Weyl groupoids. This is motivation enough to investigate simplicial arrangements from this new viewpoint, especially since it is still an open question whether the catalogue of Grünbaum is complete.