THE NONCOMMUTATIVE GEOMETRY OF THE QUANTUM PROJECTIVE PLANE

Abstract

We study the spectral geometry of the quantum projective plane [Formula: see text], a deformation of the complex projective plane ℂP2, the simplest example of spin c manifold which is not spin. In particular, we construct a Dirac operator D which gives a 0+-summable triple, equivariant under Uq(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.