Noncommutative Riemannian and Spin Geometry of the Standard q-Sphere
| dc.creator | Majid, S. | |
| dc.date | 2003-07-27 | |
| dc.date | 2003-08-04 | |
| dc.date.accessioned | 2026-07-07T04:59:55Z | |
| dc.date.available | 2026-07-07T04:59:55Z | |
| dc.description | 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 $Ω^{0,1}\oplusΩ^{1,0}$ 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. | |
| dc.description | 28 pages amslatex, added projectors and trivialisation | |
| dc.identifier | https://arxiv.org/abs/math/0307351 | |
| dc.identifier | http://arxiv.org/abs/math/0307351 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68181 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.title | Noncommutative Riemannian and Spin Geometry of the Standard q-Sphere | |
| dc.type | text |