Hilbert space representations of cross product algebras II
Konrad Schmuedgen, Elmar Wagner
Abstract
In this paper, we study and classify Hilbert space representations of cross product *-algebras of the quantized enveloping algebra Uq(e2) with the coordinate algebras O(Eq(2)) of the quantum motion group and O(q) of the complex plane, and of the quantized enveloping algebra Uq(su1,1) with the coordinate algebras O(SUq(1,1)) of the quantum group SUq(1,1) and O(Uq) of the quantum disc. Invariant positive functionals and the corresponding Heisenberg representations are explicitely described.
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