Narrow Results

Using non-canonical braidings, we first introduce a notion of symmetric tensors and corresponding Hodge operators on a class of left-covariant 3d differential calculi over SU_q(2), then we induce Hodge operators on the left-covariant 2d exterior algebra over the Podles quantum sphere.

Using a non-canonical braiding over the three-dimensional left covariant calculus we present a family of Hodge operators on SU_q(2) and on its homogeneous quantum space .

We describe how it is possible to define a Hodge–de Rham Dirac operator associated to a suitable Cartan-Killing metric form upon the exterior algebra over the quantum spheres ${\mathrm{\text{SU}}}_q(2)$ equipped with a three-dimensional left covariant calculus.