论文标题
八元和两个严格投影的紧密5设计
Octonions and the two strictly projective tight 5-designs
论文作者
论文摘要
除了常规的六角形和二十面体的顶点外，精确地进行了两个严格的射击紧密的5个设计：一个是由水ech晶格的短载体构造的，另一个是对应于八颗射击平面中广义的六边形结构的。本文介绍了这两个严格投影的紧密5型设计之间的新联系 - 使用八元的常见结构。在三维八度载体矢量空间上，某些八元相关矩阵法案在八度投影平面上产生了第一个5设计和这些相同的矩阵，以产生第二个5设计。该结果使用了由于罗伯特·威尔逊（Robert Wilson）而导致的水ech晶格的八度结构，并在广义的六边形GH（2,8）和水ech晶格之间提供了新的联系。
In addition to the vertices of the regular hexagon and icosahedron, there are precisely two strictly projective tight 5-designs: one constructed from the short vectors of the Leech lattice and the other corresponding to a generalized hexagon structure in the octonion projective plane. This paper describes a new connection between these two strictly projective tight 5-designs -- a common construction using octonions. Certain octonion involutionary matrices act on a three-dimensional octonion vector space to produce the first 5-design and these same matrices act on the octonion projective plane to produce the second 5-design. This result uses the octonion construction of the Leech lattice due to Robert Wilson and provides a new link between the generalized hexagon Gh(2,8) and the Leech lattice.
