Georgia Benkart, Samuel A. Lopes, Matthew Ondrus
Published 2012-12-06, updated 2013-04-09Version 2
An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra A_h generated by elements x,y, which satisfy yx-xy = h, where h is in F[x]. When h is nonzero, these algebras are subalgebras of the Weyl algebra A_1 and can be viewed as differential operators with polynomial coefficients. In previous work, we studied the structure of A_h and determined its automorphism group and the subalgebra of invariants under the automorphism group. Here we determine the irreducible A_h-modules. In a sequel to this paper, we completely describe the derivations of A_h over any field.
Comments: 30 pages, a few of the sections have been placed in a different order at the suggestion of the referee
A multiparameter family of irreducible representations of the quantum plane and of the quantum Weyl algebra
Irreducible representations of the quantum Weyl algebra at roots of unity given by matrices
The Derivation algebra and automorphism group of the generalized Ramond N=2 superconformal algebra
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