Elmar Wagner

Hilbert space representations of cross product algebras

In this paper, we study and classify Hilbert space representations of cross product \(\ast\)-algebras of the quantized enveloping algebra \({\user1{\mathcal{U}}}_{q} {\left( {{\text{e}}_{{\text{2}}} } \right)}\) with the coordinate algebras \({\user1{\mathcal{O}}}{\left( {{\text{E}}_{q} {\left( 2 \right)}} \right)}\) of the quantum motion group and \({\user1{\mathcal{O}}}{\left( {\mathbb{C}_{q} } \right)}\) of the complex plane, and of the quantized enveloping algebra \({\user1{\mathcal{U}}}_{q} {\left( {{\text{su}}_{{1,1}} } \right)}\) with the coordinate algebras \({\user1{\mathcal{O}}}{\left( {{\text{SU}}_{q} {\left( {1,1} \right)}} \right)}\) of the quantum group \(\mathrm{SU}_q(1,1)\) and \({\user1{\mathcal{O}}}{\left( {{\text{U}}_{p} } \right)}\) of the quantum disc. Invariant positive functionals and the corresponding Heisenberg representations are explicitly described.

Examples of Twisted Cyclic Cocycles from Covariant Differential Calculi

AbstractFor two covariant differential *-calculi, the twisted cyclic cocycle associated with the volume form is represented in terms of commutators

Representations of quantum SU(2) operators on a local chart

\left[ {\mathcal{F},\rho \left( x \right)} \right]

An operator-theoretic approach to invariant integrals on quantum homogeneous SU n,1 -spaces

for some self-adjoint operator

Representations of cross product algebras of Podles quantum spheres

\mathcal{F}

Operator representations of cross product algebras of Podles' quantum spheres

and some *-representation ρ of the underlying *-algebra.