Journal of Noncommutative Geometry


Full-Text PDF (271 KB) | Table of Contents | JNCG summary
Volume 1, Issue 2, 2007, pp. 213–239
DOI: 10.4171/JNCG/5

Dirac operators on all Podleś quantum spheres

Francesco D'Andrea (1), Ludwik Dąbrowski (2), Giovanni Landi (3) and Elmar Wagner (4)

(1) Dipartimento di Matematica, Università degli Studi di Napoli “Federico II”, Piazzale Tecchio, 80, 80125, NAPOLI, ITALY
(2) SISSA, via Bonomea, 265, 34136, TRIESTE, ITALY
(3) Dipartimento di Matematica e Informatica, Università di Trieste, Via A. Valerio, 12/1, 34127, TRIESTE, ITALY
(4) Dipartimento di Matematica e Informatica, Università di Trieste, Via Valerio, 12/1, I-34127, TRIESTE, ITALY

We construct spectral triples on all Podleś quantum spheres S2qt. These noncommutative geometries are equivariant for a left action of $\mathcal{U}$q(su(2)) and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the sphere S2. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order.

Keywords: Noncommutative geometry, spectral triples, quantum groups, quantum spheres