Hilbert space representations of cross product algebras II

الأصل · EN

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() 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.