NONCOMMUTATIVE RICCI CURVATURE AND DIRAC OPERATOR ON Cq[SL2] AT ROOTS OF UNITY
نویسنده
چکیده
We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group Cq[SL2], using a recent frame bundle formulation. We find that its covariant Ricci curvature is essentially proportional to the metric (i.e. an Einstein space). We compute the Dirac operator D/ and find for q an odd r’th root of unity that its eigenvalues are given by q-integers [m]q for m = 0, 1, · · · , r − 1 offset by the constant background curvature. We fully solve the Dirac equation for r = 3.
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