Representations of cross product algebras of Podles quantum spheres

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dc.creatorSchmuedgen, Konrad
dc.creatorWagner, Elmar
dc.date2003-05-22
dc.date2007-07-23
dc.date.accessioned2026-07-07T08:19:29Z
dc.date.available2026-07-07T08:19:29Z
dc.descriptionHilbert space representations of the cross product *-algebras of the Hopf *-algebra U_q(su_2) and its module *-algebras O(S^2_{qr}) 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(SU_q(2)) of the quantum group SU_q(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 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 U_q(su_2) are given. The invariant state h on O(S^2_{qr}) is studied in detail. By passing to function algebras over the quantum spheres S^2_{qr}, we give chart descriptions of quantum line bundles and describe the representations from the first approach by means of the second approach.
dc.description50 pages, references updated, typos corrected
dc.identifierhttps://arxiv.org/abs/math/0305309
dc.identifierhttp://arxiv.org/abs/math/0305309
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134780
dc.subjectQuantum Algebra
dc.subjectOperator Algebras
dc.subject17B37; 81R50; 46L87
dc.titleRepresentations of cross product algebras of Podles quantum spheres
dc.typetext

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