The Noncommutative Geometry of the Quantum Projective Plane
Quantum Algebra
2008-12-18 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We study the spectral geometry of the quantum projective plane CP^2_q, a deformation of the complex projective plane CP^2, the simplest example of a spin^c manifold which is not spin. In particular, we construct a Dirac operator D which gives a 0^+ summable spectral triple, equivariant under U_q(su(3)). The square of D is a central element for which left and right actions on spinors coincide, a fact that is exploited to compute explicitly its spectrum.
Cite
@article{arxiv.0712.3401,
title = {The Noncommutative Geometry of the Quantum Projective Plane},
author = {Francesco D'Andrea and Ludwik Dabrowski and Giovanni Landi},
journal= {arXiv preprint arXiv:0712.3401},
year = {2008}
}
Comments
v2: 26 pages. Paper completely reorganized; no major change, several minor ones