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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Original Russian Text Copyright © 2009 Garipov R. M. and Churkin V. A.
The authors were supported by the State Maintenance Program for the Leading Scientific Schools (Grant NSh-344.2008.1).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 4, pp. 780–799, July–August, 2009.
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Garipov, R.M., Churkin, V.A. Quasicrystallographic groups on Minkowski spaces. Sib Math J 50, 616–631 (2009). https://doi.org/10.1007/s11202-009-0069-5
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DOI: https://doi.org/10.1007/s11202-009-0069-5