Dirac operators on the quantum group SU(2) and the quantum sphere

Journal of Mathematical Sciences

Volumn 100, Issue 2, 2000, Pages 2039-2050

  Bibikov, P N ^a   Kulish, P P ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 52849136357     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/BF02675726     Document Type: Article

References (16)

1. A. Connes, Noncommutative Geometry, Academic Press, New York (1994).
2. N. Yu. Reshetikhin, L. A. Takhtajan, and L. D. Faddeev, "Quantum Lie groups and quantum Lie algebras," Algebra Analiz, 1, 178-206 (1989).
3. P. Podles, "Quantum spheres," Lett Math. Phys., 14, 193-202, (1987).
4. M. Jimbo, "A q-difference analogue of U(g) and the Yang-Baxter equation," Lett Math. Phys., 10, 63-69 (1985).
5. K. Ohta and H. Suzuki, "Dirac operators on quantum two spheres," Mod. Phys. Lett. A, 141, 2325-2333 (1994).
6. A. Yu. Alekseev and L. D. Faddeev, "A toy model for conformal field theory," Commun. Math. Phys., 141, 413-422 (1991).
7. P. Shupp, P. Watts, and B. Zumino, "Bicovariant quantum algebras and quantum Lie algebras," Commun. Math. Phys., 157, 305-329 (1993).
8. P. P. Kulish and R. Sasaki, "Covariance properties of reflection equation algebras," Progr. Theor. Phys., 89, 741-761 (1993).
9. P. P. Kulish, "Quantum groups, q-oscillators, and covariant algebras," Teor. Mat. Fiz., 94, 193-199 (1993).
10. L. L. Vaksman and Ya. S. Soibelman, "A function algebra on the quantum group SU(2)," Funkts. Anal. Prilozhen., 22, 1-14 (1988).
11. M. Noumi and K. Mimachi, "Rogers's q-ultraspherical polynomials on a quantum 2-sphere," Duke Math. J., 63, 65-80 (1991).
12. q(2) and the little q-Jacobi polynomials," J. Funct. Anal., 99, 357-386 (1991).
13. N. Berline, E. Getzler, and M. Vergne, Heat Kernels and Dirac Operators, Springer-Verlag, Berlin (1992).
14. J. A. de Azcarraga, P. P. Kulish, and F. Rodenas, "Quantum groups and deformed special relativity," Fortschr. Phys., 44, 1-40 (1996).
15. H. Grosse, C. Klimcik, and P. Presnajder, "Simple field theoretical models on noncommutative manifolds," CERN-TH/95-138, hep-th/9510177; hep-th/9510083; hep-th/9505175.
16. q(sl.(2)), q-orthogonal polynomials, and invariants of links," Preprint LOMI, E-9-88 (1988), in: Infinite-Dimensional Lie Algebras and Groups, Singapore (1989).