Hilbert Space Representations of Cross Product Algebras

Details Hilbert Space Representations of Cross Product Algebras Hilbert Space Representations of Cross Product Algebras

2001-05-23

arxiv.org/abs/math/0105185v3

Mathematics

Quantum Algebra

LaTeX2e, 44 pages; appears in Journal of Functional Analysis

Scientific paper

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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