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Hilbert Space Representations of Cross Product Algebras

Konrad Schmuedgen·Elmar Wagner
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Abstract

Hilbert space representations of cross product *-algebras of the Hopf *-algebras U_q(gl_2) with the coordinate algebras O(C^2_q) and O(R^3_q) of quantum vector spaces and U_q(su_2) with coordinate algebras O(SU_q(2)) and O(S^2_q) 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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BibTeXRIS

Konrad Schmuedgen, Elmar Wagner. 2002-12-12. Hilbert Space Representations of Cross Product Algebras. https://arxiv.org/abs/math/0105185

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