LIE-ALGEBRA DEFORMATION OF DIFF (A)T(2) AND BLOCH ELECTRONS IN A CONSTANT UNIFORM MAGNETIC-FIELD

Magnetic translation operators that generate symmetries of a Bloch ele ctron in a constant uniform magnetic field are shown to span the sine bracket algebra which is the unique Lie algebra deformation of the are a-preserving diffeomorphisms of a two-torus. The deformation parameter is identified with the number of magnetic flux quanta through a unit cell of the substrate lattice. The symmetries of a spin-1/2 Bloch elec tron are shown to realize the supersymmetric extension of the sine bra cket algebra.