Portugaliae Mathematica
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Published online: 2015-10-29
A multiparameter family of irreducible representations of the quantum plane and of the quantum Weyl algebra
Samuel A. Lopes[1] and João N.P. Lourenço[2] (1) Universidade do Porto, Portugal(2) Universidade do Porto, Portugal
We construct a family of irreducible representations of the quantum plane and of the quantum Weyl algebra over an arbitrary field, assuming the deformation parameter is not a root of unity. We determine when two representations in this family are isomorphic, and when they are weight representations, in the sense of [1].
Keywords: Quantum plane, quantum Weyl algebra, irreducible representation, weight representation, infinite-dimensional representation
Lopes Samuel, Lourenço João: A multiparameter family of irreducible representations of the quantum plane and of the quantum Weyl algebra. Port. Math. 72 (2015), 407-419. doi: 10.4171/PM/1973