We introduce and investigate a one parameter family of quantum spaces invariant under the left (right) coactions of the group-like element T (j=1) h of the Jordanian function algebra Funh(SL(2)). These spaces may be regarded as Jordanian quantization of the two-dimensional spheres.

We investigate the spin 1/2 fermions on quantum two spheres. It is shown that the wave functions of fermions and a Dirac Operator on quantum two spheres can be constructed in a manifestly covariant way under the quantum group SU(2) q. The concept of total angular momentum and chirality can be expressed by using q-analog of Pauli-matrices and appropriate commutation relations.

Noncommutative analogues of n-dimensional balls are defined by repeated application of the quantum double suspension to the classical low-dimensional spaces. In the ‘even-dimensional’ case they correspond to the Twisted Canonical Commutation Relations of Pusz and Woronowicz. Then quantum spheres are constructed as double manifolds of noncommutative balls. Both C-algebras and polynomial algebras...

A large class of noncommutative spherical manifolds was obtained recently from cohomology considerations. A one-parameter family of twisted 3-spheres was discovered by Connes and Landi, and later generalized to a three-parameter family by Connes and Dubois-Violette. The spheres of Connes and Landi were shown to be homogeneous spaces for certain compact quantum groups. Here we investigate whethe...

We construct new families of spectral triples over quantum spheres, with a particular attention focused on the standard Podleś quantum sphere and twisted Dirac operators.