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In the paper, a new method determining the wave vector star channel in thereciprocal lattice space of crystal in the light of the translational symmetrybreaking is proposed, and, in order to consider the phase transitions accordingto the wave vector star channel, the conception of wave vector star channelgroup is adopted. By this method, it is revealed that the phase transitions incrystal are induced not by any arbitrary combinations of arms of the givenstar, but by the selected combinations of arms which are satisfied by symmetryof the parent phase. The wave vector star channel group is defined as the setof elements of space group leaving the wave vector star channel invariant. Weshow that the conception of wave vector star channel group can be efficientlyused in studying the translational symmetry breaking related to all theLifshitz wave vector stars of 230 space groups.

Wave vector star channel and star channel group in the reciprocal lattice space of crystal