Quasicrystallographic groups on Minkowski spaces
Copyright policy )Quasicrystallographic groups on Minkowski spaces
Summary: We generalize the quasicrystallographic groups in the sense of Novikov and Veselov from Euclidean spaces to pseudo-Euclidean and affine spaces. We prove that the quasicrystallographic groups on Minkowski spaces whose rotation groups satisfy an additional assumption are projections of crystallographic groups on pseudo-Euclidean spaces. An example shows that the assumption cannot be dropped. We prove that each quasicrystallographic group is a projection of a crystallographic group on an affine space.
- Sobolev Institute of Mathematics Russian Federation
affine spaces, Other geometric groups, including crystallographic groups, projections, quasicrystallographic groups, modules, Discrete subgroups of Lie groups, enveloping algebras, Minkowski spaces, bilinear forms, Statistical mechanics of crystals
affine spaces, Other geometric groups, including crystallographic groups, projections, quasicrystallographic groups, modules, Discrete subgroups of Lie groups, enveloping algebras, Minkowski spaces, bilinear forms, Statistical mechanics of crystals
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