Quasicrystallographic groups on Minkowski spaces |
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Authors: | R. M. Garipov V. A. Churkin |
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Affiliation: | (1) Lavrent’ev Institute of Hydrodynamics, Novosibirsk, Russia;(2) Sobolev Institute of Mathematics, Novosibirsk, Russia |
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Abstract: | 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. |
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Keywords: | affine space Minkowski space quasicrystallographic group projection bilinear form enveloping algebra module |
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