Induction of quantum group representations. (English) Zbl 0962.16030
The author introduces a generalised procedure of induction of quantum group representations from coisotropic subgroups. The latter are identified with certain coalgebras determined by quantum embeddable homogeneous spaces. Main properties of such quantum induced representations are proven. In particular, the geometric meaning of the construction is revealed, by proving that the corresponding corepresentation space of the function algebra can be identified with the space of sections of a vector bundle associated to a coalgebra principal bundle over a quantum homogeneous space introduced in [T. Brzeziński and S. Majid, Commun. Math. Phys. 191, No. 2, 467-492 (1998; Zbl 0899.55010); T. Brzeziński, J. Algebra 215, No. 1, 290-317 (1999; Zbl 0936.16030)].
Reviewer: Tomasz Brzeziński (Swansea)
MSC:
| 16W35 | Ring-theoretic aspects of quantum groups (MSC2000) |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 16W30 | Hopf algebras (associative rings and algebras) (MSC2000) |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 58B32 | Geometry of quantum groups |
Keywords:
quantum subgroups; coisotropic subgroups; induced representations; quantum bundles; quantum homogeneous spacesReferences:
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