Quantum hall effect on the hyperbolic plane

Communications in Mathematical Physics

Volumn 190, Issue 3, 1998, Pages 629-673

  Carey, A L ^a   Hannabuss, K C ^b   Mathai, V ^a   McCann, P ^a  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032358864     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050255     Document Type: Article

References (50)

1. Atiyah, M.F.: Elliptic operators, discrete groups and Von Neumann algebras. Astérisque no.32-33, 43-72 (1976)
2. Avron, J., Klein, M., Pnueli, A., Sedun, L.: Hall conductance and adiabatic charge transport of leaky tori. Phys. Rev. Lett. 69, 128-131 (1990)
3. Avron, J., Seiler, R., Simon, B.: Charge deficiency, charge transport and comparisons of dimension. Commun. Math. Phys. 159, 399-422 (1994)
4. Avron, J., Seiler, R., Yaffe, I.: Adiabatic theorems and applications to the integer quantum Hall effect. Commun. Math. Phys. 110, 33-49 (1987)
5. Bellissard, J.: K-theory of C*-algebras in solid state physics Springer Lecture Notes in Physics 257, 1986, pp. 99-156
6. Bellissard, J., van Elst, A., Schulz-Baldes, H.: The non-commutative geometry of the quantum Hall effect. J. Math. Phys. 35, 5373-5451 (1994)
7. Bost, J.: Principe d'Oka, K-théorie et systémes dynamiques non commutatifs. Invent. Math. 101 no. 2, 261-333 (1990)
8. Brüning, J., Sunada, T.: On the spectrum of gauge-periodic elliptic operators. Méthodes semi-classiques. Vol. 2 (Nantes, 1991). Astérisque 210, 65-74 (1992)
9. Brüning, J., Sunada, T.: On the spectrum of gauge-periodic elliptic operators. Méthodes semi-classiques. Vol. 2 (Nantes, 1991). Astérisque 210, 65-74 (1992)
10. Cheeger, J., Gromov, M., Taylor, M.: Finite propagation speed, kernel estimates for functions of the Laplace operator and the Geometry of complete Riemannian manifolds. Jour. Diff. Geom. 17, 15-54 (1982)
11. Choi, M., Elliott, G., Yui, N.: Gauss polynomials and the rotation algebra. Invent. Math. 99 no. 2, 225-246 (1990)
12. Comtet, A.: On the Landau levels on the hyperbolic plane, Ann.Phys. 173, 185-209 (1987)
13. Comtet, A., Houston, P.: Effective action on the hyperbolic plane in a constant external field. J. Math. Phys. 26, 185-191 (1985)
14. Connes, A.: Non commutative differential geometry. Publ. Math. I.H.E.S. 62, 257-360 (1986)
15. Connes, A.: Noncommutative geometry. San Diego, CA: Academic Press, Inc., 1994
16. Connes, A., Moscovici, H.: Cyclic cohomology, the Novikov conjecture and hyperbolic groups. Topology 29, 345-388 (1990)
17. Cuntz, J.: K-theoretic amenability for discrete groups. J. Reine Angew. Math. 344, 180-195 (1983)
18. Elliott, G.: On the K-theory of the C*-algebra generated by a projective representation of a torsion-free discrete group. In: Operator Algebras and Group Representations, London: Pitman, 1983, pp. 157-184
19. Green, P.: The structure of imprimitivity algebras. J. Func. Anal. 36, 88-104 (1980)
20. Griffiths, P. and Harris, J.: Principles of algebraic geometry. New York: Wiley, 1978
21. Gromov, M.: Volume and bounded cohomology. Publ. Math. I.H.E.S. 56, 5-99 (1982)
22. 2 Hodge theory. Diff. Geom. 33, 263-292 (1991)
23. Helgason, S.: Differential Geometry, Lie Groups and Symmetric Spaces. Pure and Applied Mathematics, 80, New York-London: Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], 1978
24. Iengo, R., Li, D.: Quantum mechanics and the quantum Hall effect on Riemann surfaces. Nuclear Phys. B 413, 735-753 (1994)
25. Ji, R.: Smooth dense subalgebras of reduced group C*-algebras, Schwartz cohomology of groups and cyclic cohomology. Jour. Func. Anal. 107, 1-33 (1992)
26. Julg, P., Kasparov, G.: Operator K-theory for the group SU(n, 1). J. Reine Angew. Math. 463, 99-152 (1995)
27. Kasparov, G.: Lorentz groups, K-theory of unitary representations and crossed products. Soviet Math. Dokl. 29, 256-260 (1984)
28. Kasparov, G.: K-theory, group C*-algebras and higher signatures. Conspectus, (1980), published in 'Novikov conjectures, index theorems and rigidity', vol. 1, editors S. Ferry, A. Ranicki, J. Rosenberg, Lond. Math. Soc. Lecture Note Series 226, Cambridge: Cambridge University Press, 1995
29. Kasparov, G.: K-theory, group C*-algebras and higher signatures. Conspectus, (1980), published in 'Novikov conjectures, index theorems and rigidity', vol. 1, editors S. Ferry, A. Ranicki, J. Rosenberg, Lond. Math. Soc. Lecture Note Series 226, Cambridge: Cambridge University Press, 1995
30. Kasparov, G.: Equivariant KK-theory and the Novikov conjecture. Inv. Math. 91, 147-201 (1988)
31. Klimek, S., Lesznewski, A.: Quantum Riemann surfaces I: the unit disc. Commun. Math. Phys. 146, 105-122 (1992)
32. Klimek, S., Lesznewski, A.: Quantum Riemann surfaces II: The discrete series. Lett. Math. Phys. 24, 125-139 (1992)
33. Mathai, V.: In preparation
34. McCann, P., Carey, A.: A discrete model of the integer quantum Hall effect. Publ. RIMS, Kyoto Univ. 32, 117-156 (1996)
35. Mostow, G.: Strong rigidity of symmetric spaces. Ann. Math. Studies, 78, Princeton N J: Princeton University Press 1973
36. Muhly, P., Renault, J., Williams, P.: Equivalence and isomorphism for groupoid C*-algebras. J. Operator Th. 17, 3-22 (1987)
37. Nakamura, S., Bellissard, J.: Low energy bands do not contribute to the quantum Hall effect. Commun. Math. Phys. 131, 283-305 (1990)
38. Packer, J., Raeburn, I.: Twisted cross products of C*-algebras. Math. Proc. Camb. Phil. Soc. 106, 293-311 (1989)
39. Packer, J., Raeburn, I.: On the structure of twisted group C*-algebras. Trans.Am. Math. Soc. 334, 685-718 (1992)
40. Packer, J., Raeburn, I.: Twisted cross products of C*-algebras. II, Math. Ann. 287, 595-612 (1990)
41. Renault, J.: A groupoid approach to C*-algebras. Lecture Notes in Mathematics 793, Berlin: Springer, 1980
42. Renault, J.: Représentations des produits croisés d'algèbres de groupoïdes. J.Operator Th. 18, 67-97 (1987)
43. Renault, J.: The ideal structure of groupoid crossed product C*-algebras. J. Operator Th. 25, 3-36 (1991)
44. Rieffel, M.: C*-algebras associated with irrational rotations. Pac. J. Math. 93, 415-429 (1981)
45. Rosenberg, J.: Continuous trace algebras from the bundle theoretic point of view. Jour. Aus. Math. Soc. 47, 368-381 (1989)
46. Shubin, M.: Discrete Magnetic Schrödinger operators. Commun. Math. Phys. 164, no.2, 259-275 (1994)
47. Singer, I.M.: Some remarks on operator theory and index theory. Springer Lecture Notes in Math. 575, 1977, 128-137
48. Sunada, T.: A discrete analogue of periodic magnetic Schrödinger operators. Contemp. Math. 173, 283-299 (1994)
49. Takesaki, M.: Theory of operator algebras I. New York: Springer-Verlag, 1979)
50. Xia, J.: Geometric invariants of the quantum hall effect. Commun. Math. Phys. 119, 29-50 (1988)