An Ore extension over a polynomial algebra F[x] is either a quantum plane, aquantum Weyl algebra, or an infinite-dimensional unital associative algebra A_hgenerated by elements x,y, which satisfy yx-xy = h, where h is in F[x]. When his nonzero, these algebras are subalgebras of the Weyl algebra A_1 and can beviewed as differential operators with polynomial coefficients. In previouswork, we studied the structure of A_h and determined its automorphism group andthe subalgebra of invariants under the automorphism group. Here we determinethe irreducible A_h-modules. In a sequel to this paper, we completely describethe derivations of A_h over any field.
展开▼
