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We calculate the torsion free spin connection on the quantum group B q [SU 2] at the fourth root of unity. From this we deduce the covariant derivative andthe Riemann curvature. Next we compute the Dirac operator of this quantum groupand we give numerical approximations of its eigenvalues.

Noncommutative ricci curvature and dirac operator on B q [SU 2 ] at the fourth root of unity