Geodesic
Dirac operators on quantum $SU(2)$ group and quantum sphere
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 14, Tome 245 (1997), pp. 49-65

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Problems of definition of Dirac operators on the quantum group $SU(2)$ and the quantum sphere $S^2_{q\mu}$ are discussed. In both two cases proposed ones have the similar $SU_q(2)$-invariant form and are strictly connected with corresponding Laplace operators. The spectrum of proposed operators also is calculated. 
@article{ZNSL_1997_245_a2,
     author = {P. N. Bibikov and P. P. Kulish},
     title = {Dirac operators on quantum $SU(2)$ group and quantum sphere},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {49--65},
     publisher = {mathdoc},
     volume = {245},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_245_a2/}
}
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P. N. Bibikov; P. P. Kulish. Dirac operators on quantum $SU(2)$ group and quantum sphere. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 14, Tome 245 (1997), pp. 49-65. http://geodesic.mathdoc.fr/item/ZNSL_1997_245_a2/