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Hilbert space representations of cross product algebras II

Konrad Schmuedgen·Elmar Wagner
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Abstract

In this paper, we study and classify Hilbert space representations of cross product *-algebras of the quantized enveloping algebra $U_q(e_2)$ with the coordinate algebras $O(E_q(2))$ of the quantum motion group and $O(\C_q)$ of the complex plane, and of the quantized enveloping algebra $U_q(su_{1,1})$ with the coordinate algebras $O(SU_q(1,1))$ of the quantum group $SU_q(1,1)$ and $O(U_q)$ of the quantum disc. Invariant positive functionals and the corresponding Heisenberg representations are explicitely described.

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Konrad Schmuedgen, Elmar Wagner. 2003-08-25. Hilbert space representations of cross product algebras II. https://arxiv.org/abs/math/0308229

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