ar X iv : m at h / 03 05 30 9 v 1 [ m at h . Q A ] 2 2 M ay 2 00 3 Representations of cross product algebras of Podles ’ quantum spheres
نویسنده
چکیده
Hilbert space representations of the cross product ∗-algebras of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(Sqr) of Podles’ spheres are investigated and classified by describing the action of generators. The representations are analyzed within two approaches. It is shown that the Hopf ∗-algebra O(SUq(2)) of the quantum group SUq(2) decomposes into an orthogonal sum of projective Hopf modules corresponding to irreducible integrable ∗-representations of the cross product algebras and that each irreducible integrable ∗-representation of the first approach appears with multiplicity one. The projections of these projective modules are computed. The decompositions of tensor products of irreducible integrable ∗-representations with spin l representations of Uq(su2) are given. The invariant state h on O(Sqr) and the Heisenberg representation are studied in detail.
منابع مشابه
ar X iv : m at h / 03 05 30 9 v 3 [ m at h . Q A ] 2 3 Ju l 2 00 7 Representations of cross product algebras of Podleś quantum spheres
Hilbert space representations of the cross product ∗-algebras of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(Sqr) of Podleś spheres are investigated and classified by describing the action of generators. The representations are analyzed within two approaches. It is shown that the Hopf ∗-algebra O(SUq(2)) of the quantum group SUq(2) decomposes into an orthogonal sum of projective Hopf...
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