Representation of Crystallographic Subperiodic Groups in Clifford's Geometric Algebra

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 .Comment: 17 pages, 6 figures, 11 tables. arXiv admin note: substantial text overlap with arXiv:1306.128

Representation of Crystallographic Subperiodic Groups by Geometric Algebra

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).Comment: 11 pages, 5 figures, 9 table