The Noncommutative Geometry of the Quantum Projective Plane
Abstract
We study the spectral geometry of the quantum projective plane CP2q, a deformation of the complex projective plane CP2, the simplest example of a spinc manifold which is not spin. In particular, we construct a Dirac operator D which gives a 0+ summable spectral 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.
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