Crystallographic Restrictions for Colour Lattices with Modular Sublattices

2002/05/14 by Leonid G. Fel, Fel, Leonid G.
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #math-ph #math.GR #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0205020

18 pages, 2 figures

arxiv created 2002/05/14 · arxiv updated 2009/11/30

Abstract

The \em d -- dimensional n -- colour lattice \bf \BbbL^d with modular sublattices are studied, when the only one crystallographic type of sublattices does exist and the only one of the colours occupies a sublattice, which is still invariant under k--fold rotation C_k. Such kind of colouring always preserves an equal fractions of the colours composed \bf \BbbL^d. The n -- colour lattice with modular sublattices allow to exist the crystallographic rotations C_k for k=p^r, r≥ 1 and n≤ p, where p is a prime number.

Related

• Finite diamond-colored modular and distributive lattices with\n applications to combinatorial Lie representation theory
• The Shadow Theory of Modular and Unimodular Lattices
• On colourings of cubic lattices
• On a characterization of o-modular semilattices
• Tiling the integer lattice with translated sublattices