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

This article is cited in 4 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.

UDC: 512.865.3

Received: 07.05.2007


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

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