arXiv math/03082292003-08-25math.QA

Hilbert space representations of cross product algebras II

Konrad Schmuedgen, Elmar Wagner

备注：: 42 pages

英文摘要：

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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