After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a first example we show that the su(2) symmetry of the QHE on sphere leads to su q (2) algebra in the equator . We explain this result by a contraction of su(2) . Secondly , with the help of the symmetry operators of QHE on the Pioncare upper half plane , we will show that the ground state wave functions form a representation of the su q (2) algebra .

Abstract. For a real Hilbert space (H, ,

For a nondecreasing function K : [0, ∞) → [0, ∞) and 0 < p < ∞ , −2 < q < ∞ , we introduce QK(p, q), a QK type space of functions analytic in the unit disk and study the characterizations of QK (p, q). Necessary and sufficient conditions on K such that QK(p, q) become some known spaces are given.

In this paper we provide an algebraic definition for the Schouten product and give a decomposition for homogeneous Poisson structures in any n-dimensional vector space. A large class of n-homogeneous Poisson structures in ℝk is also characterised.