Noncommutative Riemannian and Spin Geometry of the Standard q-Sphere

Details Noncommutative Riemannian and Spin Geometry of the Standard q-Sphere Noncommutative Riemannian and Spin Geometry of the Standard q-Sphere

2003-07-27

arxiv.org/abs/math/0307351v2

Mathematics

Quantum Algebra

28 pages amslatex, added projectors and trivialisation

Scientific paper

We study the quantum sphere $C_q[S^2]$ as a quantum Riemannian manifold in the quantum frame bundle approach. We exhibit its 2-dimensional cotangent bundle as a direct sum $\Omega^{0,1}\oplus\Omega^{1,0}$ in a double complex. We find the natural metric, volume form, Hodge * operator, Laplace and Maxwell operators. We show that the q-monopole as spin connection induces a natural Levi-Civita type connection and find its Ricci curvature and q-Dirac operator $D$. We find the possibility of an antisymmetric volume form quantum correction to the Ricci curvature and Lichnerowicz-type formulae for $D^2$. We also remark on the geometric q-Borel-Weil-Bott construction.

Affiliated with

Also associated with

No associations

Rating

Noncommutative Riemannian and Spin Geometry of the Standard q-Sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Noncommutative Riemannian and Spin Geometry of the Standard q-Sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Noncommutative Riemannian and Spin Geometry of the Standard q-Sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-712674