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THE NONCOMMUTATIVE GEOMETRY OF THE QUANTUM PROJECTIVE PLANE

FRANCESCO D'ANDREA

Département de Mathématique, Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348, Louvain-La-Neuve, Belgium

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LUDWIK DABROWSKI

Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, I-34014, Trieste, Italy

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GIOVANNI LANDI

Dipartimento di Matematica e Informatica, Università di Trieste, Via A. Valerio 12/1, I-34127, Trieste, Italy

INFN, Sezione di Trieste, Trieste, Italy

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https://doi.org/10.1142/S0129055X08003493Cited by:28 (Source: Crossref)

Abstract

We study the spectral geometry of the quantum projective plane , 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 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.

Keywords:

AMSC: 58B34, 17B37

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