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Sibirskii Matematicheskii Zhurnal, 2009, Volume 50, Number 4, Pages 780–799 (Mi smj2000)  
This article is cited in 1 scientific paper (total in 1 paper)

Quasicrystallographic groups on Minkowski spaces

R. M. Garipova, V. A. Churkinb

a M. A. Lavrent'ev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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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.
Keywords: affine space, Minkowski space, quasicrystallographic group, projection, bilinear form, enveloping algebra, module.
Received: 25.04.2008
English version:
Siberian Mathematical Journal, 2009, Volume 50, Issue 4, Pages 616–631
DOI: https://doi.org/10.1007/s11202-009-0069-5
Bibliographic databases:
UDC: 512
Language: Russian
Citation: R. M. Garipov, V. A. Churkin, “Quasicrystallographic groups on Minkowski spaces”, Sibirsk. Mat. Zh., 50:4 (2009), 780–799; Siberian Math. J., 50:4 (2009), 616–631
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/smj/v50/i4/p780
    • This publication is cited in the following 1 articles:
    1. V. A. Churkin, “The weak Bieberbach theorem for crystallographic groups on pseudo-Euclidean spaces”, Siberian Math. J., 51:3 (2010), 557–568  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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    References:89
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