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Properties of the magnetic translation operators for a charged particlemoving in a crystalline potential and a uniform magnetic field show that it isnecessary to consider all inequivalent irreducible projective representationsof the the crystal lattice translation group. These considerations lead to theconcept of magnetic cells and indicate the periodicity of physical propertieswith respect to the charge. It is also proven that a direct product of suchrepresentations describe a system of two (many, in general) particles.Therefore, they can be applied in description of interacting electrons in amagnetic field, for example in the fractional quantum Hall effect.Comment: IOPP sty + AM

Algebraic description of a two-dimensional system of charged particles in an external magnetic field and periodic potential