Affine subgroups of the affine Coxeter group with the same Coxeter number
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917412188717056 |
|---|---|
| author | Koca, Nazife Ozdes Koca, Mehmet |
| author_facet | Koca, Nazife Ozdes Koca, Mehmet |
| contents | Affine subgroups having the same Coxeter number with the affine Coxeter groups W(An), W(Dn), and W(En) are constructed by graph folding technique. The affine groups W(Cn) and W(Bn) are obtained from the Coxeter groups W(A2n-1) and W(D2n-1) respectively. The affine groups W(E6), W(D6) and W(E8) lead to the affine groups W(F4), W(H3), and W(H4) respectively by graph folding. The latter two are the non-crystallographic groups where W(H3) plays a special role in the quasicrystallographic structures with icosahedral symmetry. A general construction of the affine dihedral subgroups is introduced, some of which, describe the existing planar quasicrystallography. In the construction of the root systems, sets of orthonormal vectors are used but a special non-orthogonal set of vectors in the formulation of the root system of W(An) is also introduced which has practical applications in the construction of the lattices An and An* and their Delone and Voronoi cells. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine subgroups of the affine Coxeter group with the same Coxeter number Koca, Nazife Ozdes Koca, Mehmet Mathematical Physics Other Condensed Matter 52B10, 52B11, 52B15 Affine subgroups having the same Coxeter number with the affine Coxeter groups W(An), W(Dn), and W(En) are constructed by graph folding technique. The affine groups W(Cn) and W(Bn) are obtained from the Coxeter groups W(A2n-1) and W(D2n-1) respectively. The affine groups W(E6), W(D6) and W(E8) lead to the affine groups W(F4), W(H3), and W(H4) respectively by graph folding. The latter two are the non-crystallographic groups where W(H3) plays a special role in the quasicrystallographic structures with icosahedral symmetry. A general construction of the affine dihedral subgroups is introduced, some of which, describe the existing planar quasicrystallography. In the construction of the root systems, sets of orthonormal vectors are used but a special non-orthogonal set of vectors in the formulation of the root system of W(An) is also introduced which has practical applications in the construction of the lattices An and An* and their Delone and Voronoi cells. |
| title | Affine subgroups of the affine Coxeter group with the same Coxeter number |
| topic | Mathematical Physics Other Condensed Matter 52B10, 52B11, 52B15 |
| url | https://arxiv.org/abs/2406.17509 |