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arXiv · 0712.3401

The Noncommutative Geometry of the Quantum Projective Plane

Francesco D'Andrea·Ludwik Dabrowski·Giovanni Landi
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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.

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Francesco D'Andrea, Ludwik Dabrowski, Giovanni Landi. 2008-09-08. The Noncommutative Geometry of the Quantum Projective Plane. https://doi.org/10.1142/s0129055x08003493

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