Representations of cross product algebras of Podles quantum spheres

Details Representations of cross product algebras of Podles quantum spheres Representations of cross product algebras of Podles quantum spheres

2003-05-22

arxiv.org/abs/math/0305309v3

Mathematics

Quantum Algebra

50 pages, references updated, typos corrected

Scientific paper

Hilbert 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.

Affiliated with

Also associated with

No associations

Rating

Representations of cross product algebras of Podles quantum spheres does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Representations of cross product algebras of Podles quantum spheres, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations of cross product algebras of Podles quantum spheres will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-41272