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Algebra Logika, 2008, Volume 47, Number 1, Pages 31–53 (Mi al344)  

This article is cited in 3 scientific papers (total in 3 papers)

Crystallographic classes in a 4-dimensional Minkovskii space

R. M. Garipov

M. A. Lavrent'ev Institute of Hydrodynamics

Abstract: On a crystallographic group, a condition of being topologically discrete is imposed which is weaker than is the conventional requirement for an action on space to be discontinuous. Isomorphism classification is given for crystallographic groups in three crystallographic classes in a 4-dimensional Minkovskii space, which are defined by unimodular subgroups of the general Lorentz group. In these classes are, respectively, 24, 36, and 68 crystallographic groups.

Keywords: crystallographic group, Minkovskii space, general Lorentz group.

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English version:
Algebra and Logic, 2008, 47:1, 18–31

Bibliographic databases:

UDC: 512.865.3
Received: 07.05.2007

Citation: R. M. Garipov, “Crystallographic classes in a 4-dimensional Minkovskii space”, Algebra Logika, 47:1 (2008), 31–53; Algebra and Logic, 47:1 (2008), 18–31

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. M. Garipov, V. A. Churkin, “Quasicrystallographic groups on Minkowski spaces”, Siberian Math. J., 50:4 (2009), 616–631  mathnet  crossref  mathscinet  isi  elib  elib
    2. 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
    3. R. M. Garipov, “Volnovaya interpretatsiya effekta Messbauera”, Sib. zhurn. industr. matem., 13:3 (2010), 6–12  mathnet
  • Алгебра и логика Algebra and Logic
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