Similar Submodules and Coincidence Site Modules

• Authors: P. Zeiner
• Languages of publication: EN

Abstracts

EN

We consider connections between similar sublattices and coincidence site lattices and, more generally, between similar submodules and coincidence site modules of general (free) ℤ-modules in ℝ^d. In particular, we generalise results obtained by S. Glied and M. Baake on similarity and coincidence isometries of lattices and certain lattice-like modules called S-modules. An important result is that the factor group OS(M)/OC(M) is Abelian for arbitrary ℤ-modules M, where OS(M) and OC(M) are the groups of similar and coincidence isometries, respectively. In addition, we derive various relations between the indices of coincidence site lattices and their corresponding similar sublattices.

Keywords

EN

61.44.Br

Discipline

• 61.44.Br: Quasicrystals

• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 126
• Issue: 2
• Pages: 641-644

Dates

published

2014-08

Contributors

author

P. Zeiner

• Fakultät für Mathematik, Universität Bielefeld, 33615 Bielefeld, Germany

References

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Identifiers

DOI

10.12693/APhysPolA.126.641