Hilbert Space Representations of Cross Product Algebras
Konrad Schmuedgen, Elmar Wagner
Abstract
Hilbert space representations of cross product *-algebras of the Hopf *-algebras Uq(gl2) with the coordinate algebras O(C2q) and O(R3q) of quantum vector spaces and Uq(su2) with coordinate algebras O(SUq(2)) and O(S2q) of corresponding quantum spheres are investigated and classified. Invariant states on the coordinate *-algebras are described by two variants of the quantum trace.
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