Hodge duality operators on left covariant exterior algebras over two and   three dimensional quantum spheres
  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 the quantum SU(2) group, then we induce Hodge operators on the left covariant 2d exterior algebras over the standard Podles quantum sphere. 
Alessandro Zampini
math.QA hep-th math-ph math.MP