In particular, just like for motion on a cone [@Has07], symmetry manifests itself in a rather unusual way in this quantum system. In particular, due to its relevance to the quantum Hall effect, the Landau level problem has been studied very extensively (for a recent review see [@Ste08]). For example, the problem has already been investigated on a torus in [@Che95; @Zai89], however, without emphasizing the accidental symmetry aspects. In this paper, we concentrate entirely on those aspects, thus addressing an old and rather well-studied problem from an unconventional point of view.

The rest of the paper is organized as follows. In section 2 the cyclotron problem is reviewed in the infinite volume, with special emphasis on its oscillator algebras and accidental symmetry generators. In section 3 the system is put on a torus and the unusual manifestation of the accidental symmetry is worked out. Section 4 contains our conclusions.

Particle in the Infinite Volume
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In this section we review the standard knowledge about a non-relativistic particle moving in a constant magnetic field in the infinite volume. We proceed from a classical to a semi-classical, and finally to a fully quantum mechanical treatment. In particular, we emphasize the symmetry 