晶体亚周期群的几何代数表示
Representation of Crystallographic Subperiodic Groups by Geometric Algebra
摘要：
我们解释了如何在几何代数中表示3D晶体学空间群，它是进一步可能类似地表示162个所谓的亚周期群的晶体学几何代数。我们构造了一个新的紧凑的几何代数群表示符号，它允许读出完整的几何代数生成元集。为了清楚起见，我们还明确地说明选择了哪些生成器。群符号是基于几何代数中的点群用向量（Clifford群，Lipschitz元素）表示。
英文摘要：
We explain how following the representation of 3D crystallographic space groups in geometric algebra it is further possible to similarly represent the 162 socalled subperiodic groups of crystallography in geometric algebra. We construct a new compact geometric algebra group representation symbol, which allows to read off the complete set of geometric algebra generators. For clarity we moreover state explicitly what generators are chosen. The group symbols are based on the representation of point groups in geometric algebra by versors (Clifford group, Lipschitz elements).
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