Francesco D’Andrea

Learn More
We construct a family of self-adjoint operators DN , N ∈ Z, which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CP q , for any ≥ 2 and 0 < q < 1. They provide 0 +-dimensional equivariant even spectral triples. If is odd and N = 1 2 (+ 1), the spectral triple is real with KO-dimension 2 mod 8.
We construct spectral triples on all Podle´s quantum spheres S 2 qt. These noncom-mutative geometries are equivariant for a left action of 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 S 2. There is also an equivariant real structure for which both the commutant property(More)
Equivariance under the action of U q (so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S 4 q. These representations are the constituents of a spectral triple on S 4 q with a Dirac operator which is isospectral to the canonical one of the spin structure of the round sphere S 4(More)
Equivariance under the action of U q (so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the orthogonal quantum 4-sphere S 4 q. These representations are the constituents of a spectral triple on S 4 q with a Dirac operator which is isospectral to the canonical one on the round sphere S 4 and which then gives(More)
In this thesis I study various aspects of theories in the two most studied examples of non-commutative spacetimes: canonical spacetime ([x µ , x ν ] = θ µν) and κ-Minkowski spacetime ([x i , t] = κ −1 x i). In the first part of the thesis I consider the description of the propagation of " classical " waves in these spacetimes. In the case of κ-Minkowski(More)