The Dirac operator on SU q (2)

Communications in Mathematical Physics

Volumn 259, Issue 3, 2005, Pages 729-759

  Dabrowski, Ludwik ^a   Landi, Giovanni ^b,c   Sitarz, Andrzej ^d   Van Suijlekom, Walter ^a   Várilly, Joseph C ^e,f  

^a SISSA   (Italy)

^b UNIVERSITY OF TRIESTE   (Italy)

^c INFN SEZIONE DI NAPOLI   (Italy)

^d JAGIELLONIAN UNIVERSITY   (Poland)

^e UNIVERSIDAD DE COSTA RICA   (Costa Rica)

^f ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 24944556223     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-005-1383-9     Document Type: Article

References (32)

1. Bär, C.: The Dirac operator on homogeneous spaces and its spectrum on 3-dimensional lens spaces. Arch. Math. 59, 65-79 (1992)
2. q(2) and the quantum sphere. J. Math. Sci. (N.Y.) 100, 2039-2050 (2000)
3. Biedenharn, L.C., Lohe, M.A.: Quantum group symmetry and q-tensor algebras. Singapore: World Scientific, 1995
4. Biedenharn, L.C., Louck, J.D.: Angular momentum in quantum physics: theory and applications. Reading, MA: Addison-Wesley, 1981
5. Chakraborty, P.S., Pal, A.: Equivariant spectral triples on the quantum SU(2) group. K-Theory 28, 107-126 (2003)
6. q(2). http://arxiv.org/list/math.OA/0211367, 2002
7. Connes, A.: Noncommutative geometry. London, San Diego: Academic Press, 1994
8. Connes, A.: Noncommutative geometry and reality. J. Math. Phys. 36, 6194-6231 (1995)
9. q (2). J. Inst. Math. Jussieu 3, 17-68 (2004)
10. Connes, A., Landi, G.: Noncommutative manifolds, the instanton algebra and isospectral deformations. Commun. Math. Phys. 221, 141-159 (2001)
11. Da̧browski, L., Landi, G., Paschke, M., Sitarz, A.: The spectral geometry of the equatorial Podleś sphere. C. R. Acad. Sci. Paris, Ser. I 340, 819-822 (2005).
12. Da̧browski, L., Sitarz, A.: Dirac operator on the standard Podleś quantum sphere. In: Noncommutative Geometry and Quantum Groups, Banach Centre Publications 61, Hajac, P.M., Pusz, W. (eds.), Warszawa: IMPAN, 2003, pp. 49-58
13. q(2). http://arxiv.org/list/math-ph/0108003, 2001
14. Gover, A.R., Zhang, R.B.: Geometry of quantum homogeneous vector bundles and representation theory of quantum groups I. Rev. Math. Phys. 11, 533-552 (1999)
15. Gracia-Bondía, J.M., Várilly, J.C., Figueroa, H.: Elements of noncommutative geometry. Boston: Birkhäuser, 2001
16. Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete mathematics. Reading, MA: Addison-Wesley, 1989
17. Hawkins, E.: Noncommutative rigidity. Commun. Math. Phys. 246, 211-235 (2004)
18. 3. Tokyo J. Math. 23, 453-472 (2000)
19. Kassel, C.: Quantum Groups. Berlin: Springer, 1995
20. q(sl(2)), q-orthogonal polynomials and invariants of links. In: Infinite dimensional lie algebras and groups, Kac, V.G. (ed.), Singapore: World Scientific, 1989, pp. 285-339
21. Klimyk, A.U., Schmüdgen, K.: Quantum Groups and their Representations. New York: Springer, 1998
22. Krähmer, U.: Dirac operators on quantum flag manifolds. Lett. Math. Phys. 67, 49-59 (2004)
23. Majid, S.: Foundations of quantum group theory. Cambridge: Cambridge Univ. Press, 1995
24. Majid, S.: Noncommutative Riemannian and spin geometry of the standard q-sphere. Commun. Math. Phys. 256, 255-285 (2005)
25. Masuda, T., Nakagami, Y., Woronowicz, S.L.: A C*-algebraic framework for quantum groups. Int. J. Math. 14, 903-1001 (2003)
26. Neshveyev, S., Tuset, L.: A local index formula for the quantum sphere. Commun. Math. Phys. 254, 323-341 (2005)
27. Podleś, P.: Quantum spheres. Lett. Math. Phys. 14, 521-531 (1987)
28. q(2). J. Geom. Phys. 31, 241-264 (1999)
29. Schmüdgen, K., Wagner, E.: Dirac operator and a twisted cyclic cocycle on the standard Podleś quantum sphere. J. reine angew. Math. 574, 219-235 (2004)
30. Sitarz, A.: Equivariant spectral triples. In: Noncommutative geometry and quantum groups, banach centre publications 61, Hajac, P.M. Pusz, W. (eds.), Warszawa: IMPAN, 2003, pp. 231-263
31. Takesaki, M.: Tomita's theory of modular Hilbert algebras. Lecture Notes in Mathematics 128, Berlin: Springer, 1970
32. Woronowicz, S.L.: Compact quantum groups. In: Quantum symmetries, Connes, A., Gawȩdski, K., Zinn-Justin, J. (eds.), Amsterdam: Elsevier Science, 1998, pp. 845-884