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

TL;DR

This paper computes the torsion-free spin connection, covariant derivative, Riemann curvature, and Dirac operator on the quantum group B_q[SU(2)] at the fourth root of unity, providing numerical eigenvalue approximations.

Contribution

It presents the first detailed calculation of geometric structures and the Dirac operator on B_q[SU(2)] at a root of unity, including numerical eigenvalue analysis.

Findings

Explicit torsion-free spin connection derived

Covariant derivative and Riemann curvature computed

Eigenvalues of the Dirac operator approximated numerically

Abstract

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 and the Riemann curvature. Next we compute the Dirac operator of this quantum group and we give numerical approximations of its eigenvalues.