The Noncommutative Geometry of the Quantum Projective Plane

Details The Noncommutative Geometry of the Quantum Projective Plane The Noncommutative Geometry of the Quantum Projective Plane

2007-12-20

arxiv.org/abs/0712.3401v2

Rev.Math.Phys.20:979-1006,2008

Mathematics

Quantum Algebra

v2: 26 pages. Paper completely reorganized; no major change, several minor ones

Scientific paper

10.1142/S0129055X08003493

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.

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