Heisenberg Double of the Generalized Quantum Euclidean Group and Its Representations

The generalized quantum Euclidean group Oq(bm,n) is a natural generalization of the quantum Euclidean group Oq(b1,1) . The Heisenberg double Dq(bm,n) of Oq(bm,n) is the smash product of Oq(bm,n) with its Hopf dual Uq(bm,n) . In this paper, we study the weight modules, the prime spectrum and the automorphism group of the Heisenberg double Dq(bm,n) .