Arithmetic Classification of Pairs (L, H)
Chapter
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Abstract
Let L be a lattice in \(\mathbb{R}^{3}\), and let H ≤ O(3) be a point group such that H ⋅ L = L. In this chapter, we classify pairs (L, H) up to arithmetic equivalence (defined below). The equivalence classes of pairs (L, H) are in one-to-one correspondence with isomorphism classes of split crystallographic groups (see Chap. 4).
Keywords
Equivalence Class Point Group Isomorphism Class Permutation Matrix Analogous Reasoning
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References
- [Sc80]R.L.E. Schwarzenberger, N-Dimensional Crystallography. Research Notes in Mathematics, vol. 41 (Pittman Advanced Publishing Program, Boston, Mass.-London 1980)Google Scholar
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© Springer International Publishing Switzerland 2014