晶体亚周期群在Clifford几何代数中的表示
Representation of Crystallographic Subperiodic Groups in Clifford's Geometric Algebra
摘要：
本文说明了在Clifford几何代数中三维晶体学空间群的表示之后，如何进一步用类似的方法表示Clifford几何代数中的162个所谓的晶体学亚周期群。构造了一个新的紧致几何代数群表示符号，它允许读出几何代数生成元的完整集合。此外，为了清楚起见，明确地陈述了所选择的生成器。群符号是基于在几何代数中点群的versors（Clifford单项式，Lipschitz元素）的表示。关键词：次周期群，克利福德几何代数，向量表示，frieze群，杆群，层群。
英文摘要：
This paper explains how, following the representation of 3D crystallographic space groups in Clifford's geometric algebra, it is further possible to similarly represent the 162 so called subperiodic groups of crystallography in Clifford's geometric algebra. A new compact geometric algebra group representation symbol is constructed, which allows to read off the complete set of geometric algebra generators. For clarity moreover the chosen generators are stated explicitly. The group symbols are based on the representation of point groups in geometric algebra by versors (Clifford monomials, Lipschitz elements). Keywords: Subperiodic groups, Clifford's geometric algebra, versor representation, frieze groups, rod groups, layer groups .
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