Converting three-space matrices to equivalent six-space matrices for Delone scalars in S6.
Converting three-space matrices to equivalent six-space matrices for Delone scalars in S6.
复制标题
将 S6 中的 Delone 标量的三空间矩阵转换为等效的六空间矩阵。
DOI：
10.1107/s2053273319014542
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Sauter,NicholasK
中科院分区：
文献类型：
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作者：
Andrews,LawrenceC;Bernstein,HerbertJ;Sauter,NicholasK
从中心布拉维晶格的原始单元到对应的中心单元的变换通常被列为变换三空间晶格向量的三乘三矩阵。当在六维格空间中工作时，使用这些3 × 3矩阵表示为Delone（Delaunay）约简中使用的Selling标量，可以转换为三空间表示，应用3 × 3矩阵，然后逆转换为六空间表示，但是拥有等效的六乘六矩阵并直接应用它们要简单得多。推导了从三空间矩阵到Selling标量（用空间S6表示）上相应矩阵的变换的一般形式，并列出了中心Delone类型的特定S6矩阵。(Note：在他后来的出版物中，鲍里斯·德劳内使用了他的姓氏的俄语版本，Delone。
The transformations from the primitive cells of the centered Bravais lattices to the corresponding centered cells have conventionally been listed as three-by-three matrices that transform three-space lattice vectors. Using those three-by-three matrices when working in the six-dimensional space of lattices represented as Selling scalars as used in Delone (Delaunay) reduction, one could transform to the three-space representation, apply the three-by-three matrices and then back-transform to the six-space representation, but it is much simpler to have the equivalent six-by-six matrices and apply them directly. The general form of the transformation from the three-space matrix to the corresponding matrix operating on Selling scalars (expressed in space S6) is derived, and the particular S6matrices for the centered Delone types are listed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)